Thermal models of solar still—A comprehensive review

Renewable and Sustainable Energy Reviews 47 (2015) 856–911

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Thermal models of solar still—A comprehensive review C. Elango a, N. Gunasekaran b, K. Sampathkumar a,n a b

Department of Mechanical Engineering, Tamilnadu College of Engineering, Coimbatore, Tamilnadu, India Department of Mechanical Engineering, SNS College of Engineering, Coimbatore, Tamilnadu, India

art ic l e i nf o

a b s t r a c t

Article history: Received 10 June 2014 Received in revised form 28 November 2014 Accepted 8 March 2015

Water is vital to life and supplying of potable water can hardly be overstressed in recent years. The conventional desalination processes require significant amount of energy to convert brackish water into potable water for human consumption and industry. With an extensive research on various desalination systems over the last few decades, solar desalination is one of the most promising methodologies to provide high quality water to the human community by using sustainable source. The demand for a small scale selfcontingent desalination device is the need of the hour. Solar still is an innovative device that utilizes solar energy to produce distilled water from brackish water. Numerous experimental research works have been reported in the literature to analyze the performance of various types of solar stills under local climatic conditions. Thermal models have also been presented based on energy balances and the theoretical results have been validated through experimental data by many researchers. Thermal models have a great advantage of predicting the performance of virtually designed solar stills without spending much cost and time. Accordingly, the usage of most recent theoretical attempts and proposed ideas tackling this point is limited. An attempt has been made in this article to provide a comprehensive review on thermal models developed for various types of solar stills and modifications done to improve their performance over the years. Our findings indicate that few more parameters and design aspects to be considered while designing new solar still. The efficacy of this study is that it provides energy researchers’ insights into solar still design for clean water production and, thus, it promotes commercialization of this product in rural development. Finally, some general course of action are given for the selection of solar still with flexible, consistent and robust design. Suggestions for further research are also incorporated. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Solar still Desalination Thermal model Energy balance Review

Contents 1. 2. 3. 4.

5.

6.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857 Solar still—A preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861 Need for thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861 Heat transfer mechanisms in a solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862 4.1. Modes of heat transfer in a solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862 4.1.1. Internal heat transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862 4.1.2. External heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863 4.1.3. Calculation of yield and thermal efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 4.1.4. Accuracy of thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 Thermal analysis of solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 5.1. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 5.2. Energy balance equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 Well-liked thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 6.1. Dunkle’s model [1961]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 6.2. Chen et al.’s model [1984]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 6.3. Clark’s model [1990] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 6.4. Adhikari et al.’s model [1990] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866 6.5. Kumar and Tiwari model [1996] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866

Corresponding author. Tel.: þ 91 4212332544. E-mail address: [email protected] (K. Sampathkumar).

http://dx.doi.org/10.1016/j.rser.2015.03.054 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

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6.6. Zheng Hongfei et al.’s model [2001]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 6.7. Tsilingiris model [2007] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 7. Various designs of solar still and their effect on thermal models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 7.1. Single basin single slope passive solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 7.1.1. Jute cloth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 7.1.2. Deep basin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868 7.1.3. Double glass cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868 7.1.4. Double condensing chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869 7.1.5. Floating perforated black plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870 7.1.6. Suspended absorber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870 7.1.7. Fins, sponges and wicks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871 7.1.8. Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872 7.1.9. External condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873 7.1.10. Water film cooling over glass cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874 7.1.11. Storage medium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874 7.1.12. Vapor adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875 7.1.13. External reflector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876 7.1.14. Packed layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 7.1.15. Key findings and discussion on thermal models of passive solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 7.2. Single basin single slope active solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 7.2.1. Flat plate collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 7.2.2. Evacuated tube collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881 7.2.3. Concentrator collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882 7.2.4. Solar pond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883 7.2.5. Heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884 7.2.6. Hybrid PV/T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885 7.2.7. Key findings and discussion on thermal models of active solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887 7.3. An assortment of new solar still designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 7.3.1. Single basin double slope solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 7.3.2. Multi-basin solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891 7.3.3. Double basin double slope solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893 7.3.4. Multi-effect solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893 7.3.5. Multistage solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896 7.3.6. Tilted wick solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898 7.3.7. Multi-wick solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899 7.3.8. Tubular solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899 7.3.9. Inverted absorber solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 7.3.10. Pyramid shaped solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 7.3.11. Triangular solar still. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 7.3.12. Stepped solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904 7.3.13. Weir type solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905 7.3.14. Inverted trickle solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906 7.3.15. Inclined solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907 7.3.16. Key findings and discussion on thermal models of new designs of solar still . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908 8. Scope for further research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909 Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 910

1. Introduction Water is a precious natural gift and an important renewable resource having several intrinsic advantages for human use. We are living today, in a ravenous world. The availability of clean and pure drinking water is the most urgent need for human community in many countries. The polluted water is not only devastating the people but also to all living things in this world. More seriously, it is a hazard to human health and nobody can escape from its horrible effects. The water-borne diseases are highly infectious which spread through contaminated water. The pure water is also needed for the areas like hospitals and dispensaries, chemical industries, battery maintenance, laboratories, etc. In developing and underdeveloped countries, the ground water resource is currently being depleted at a faster rate rather than the replenishment as compared to developed countries. The excessive use of chemical fertilizers and pesticides for agriculture is also an important reason to pollute the exhausting underground water. Indian villages are posed with overexploitation of ground water

due to increasing dependence on it as other fresh water resources are dwindling fast [1]. This problem could be partially tackled by deriving the potable water from available brackish water with the help of technology developed by the scientists and researchers. Safe drinking water from available water sources should be made by the application of eco-friendly technologies with least financial resources. Kalogirou [2] reviewed a large variety of systems, both conventional and renewable energy, used to convert sea water into fresh water suitable for human use. The conventional water distillation processes consume larger amount of energy to separate a portion of pure water from the brackish water. The physical change in the state of water as well as filtering via membrane processes, such as Multi-Stage Flash (MSF) distillation, Multiple Effect Distillation (MED), Vapor Compression (VC) distillation, Reverse Osmosis (RO), and Electro-dialysis (ED) are most often used to treat brackish water. Some of these processes are complex, requiring skilled operation and maintenance, and not considered to be energy efficient and economical.

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C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

Nomenclature: Symbols A Aa AC Ah At Ar A0 N AB b bwf C, Cp Cdiff Cr d df dncz dfw dw dt D e f f1 f2 F Fn FR F0 Gr h hb hfg hc,c–pl hc,c2–a hc,fa–w hc,pl–w hc,p–wl hc,p–wu hc,go–a hc,w–g hc,w–gi hcd,gi–go he,w–co he,w–g he,w–g1

area (m2) aperture area of solar collector (m2) area of solar collector (m2) area of water directly receiving rays (m2) circumferential area of each tubular absorber in ETC (m2) receiver area of concentrating collector (m2) area of projection of north wall (m2) absorptance (with indices for different surfaces) width of the still (m) thickness of water film (m) specific heat capacity (J/kg K) coefficient of diffusion concentration ratio thermal diffusivity (m2/s) average spacing between water and glass cover (m) vertical extent of non-convective zone in solar pond (m) thickness of flowing water (m) depth of water mass (m) time interval (s) diameter of the heat exchanger tube (m) root mean square (RMS) of percentage deviation sticking coefficient first cover fractional length (dimensionless) second cover fractional length (dimensionless) shape factor solar fraction on the north wall of still heat removal factor collector or concentrator efficiency factor Grashof number heat transfer coefficient (W/m2 K) heat transfer coefficient between basin liner and ambient (W/m2 K) latent heat of vaporization (J/kg) convective heat transfer coefficient from cell to absorber plate (W/m2 K) convective heat transfer coefficient from condensing cover-II to ambient (W/m2 K) convective heat transfer coefficient from floating absorber to basin water (W/m2 K) convective heat transfer coefficient from absorber plate to water in tubes (W/m2 K) convective heat transfer coefficient from suspended plate to lower water column (W/m2 K) convective heat transfer coefficient from suspended plate to upper water column (W/m2 K) convective heat transfer coefficient from glass cover outer surface to ambient (W/m2 K) convective heat transfer coefficient from water to glass cover (W/m2 K) convective heat transfer coefficient from water to glass inner surface(W/m2 K) conductive heat transfer coefficient from glass inner surface to glass outer surface (W/m2 K) evaporative heat transfer coefficient from water to condenser (W/m2 K) evaporative heat transfer coefficient from water to glass cover (W/m2 K) evaporative heat transfer coefficient from water to glass cover 1 (W/m2 K)

he,w–gi hr,go–a hr,w–g hr,w–gi ht,b–a ht,g1–g2 ht,g2–a ht,go–a ht,w–g ht,w–gi ht,w–g1 hw h(z) I(t) I(t)C I(t)h I(t)s Ieff K Kf lb lm L Lc Lhx Lt Le m mew mew,ju _ m M Mequ Mew Mo Moew n nr N Ntc p P Pa Pd

evaporative heat transfer coefficient from water to glass cover inner surface (W/m2 K) radiative heat transfer coefficient from glass cover outer surface to ambient (W/m2 K) radiative heat transfer coefficient from water to glass cover (W/m2 K) radiative heat transfer coefficient from water to glass cover inner surface (W/m2 K) total heat transfer coefficient between basin liner and atmosphere (W/m2 K) total heat transfer coefficient from glass cover 1 to glass cover 2 (W/m2 K) total heat transfer coefficient from glass cover 2 to ambient (W/m2 K) total top heat loss coefficient between glass cover outer surface and atmosphere (W/m2 K) total heat transfer coefficient from water to glass cover (W/m2 K) total heat transfer coefficient from water to glass cover inner surface (W/m2 K) total heat transfer coefficient from water to glass cover 1 (W/m2 K) convective heat transfer coefficient between basin liner and water mass (W/m2 K) fraction of solar radiation penetrating to the depth z in the solar pond intensity of solar radiation (W/m2) intensity of solar radiation on collector or concentrator panel (W/m2) intensity of solar radiation on horizontal surface (W/ m2 ) intensity of solar radiation on inclined glass cover surface of solar still (W/m2) effective solar radiation (W/m2) thermal conductivity (W/m K) thermal conductivity of humid air (W/m K) length of basin (m) height of external reflector (m) thickness (m) length of cavity (m) length of heat exchanger (m) length of trough (m) Lewis number mass per unit basin area (kg/m2) hourly yield from solar still (kg/m2 h) hourly yield from jute cloth (kg/m2 h) mass flow rate (kg/s) mass (kg) equivalent heat capacity of PCM daily yield from solar still (kg/m2 day) molecular weight (kg/mol) mass or molar flux of water evaporated per unit time (kg/m2 s or kg mol/m2 s) constant in Nusselt number expression number of reflections number of collectors number of tubes in the collector perimeter (m) saturated partial pressure (N/m2) atmospheric pressure (Pa) partial pressure of vapor at dew point temperature (Pa)

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

Pg0 Pgi PLM PT Pw Pw0 Pr qb qc,cf–a qc,go-a qc,w–g qc,w–gi qecf qe,w–g qe,w–gi qLpkd qmw qr,cf–a qr,go–a qr,w–g qr,w  gi qt,w  g qt,w  gi qu,c1–c2 qw Q Qcond Qevap Qsun,df Qsun,dr Qsun,ext Qsun,int Qu r R Rc Rh Rwall Ra Ra0 Re

saturated partial vapor pressure at glass temperature at t¼0 (N/m2) partial vapor pressure at glass inner surface temperature (N/m2) logarithmic mean pressure (Pa) total pressure (N/m2) partial vapor pressure at water surface temperature (N/m2) saturated partial vapor pressure at water temperature at t¼0 (N/m2) Prandtl number heat loss between basin liner and ambient (W/m2) convective heat transfer rate from cooling film to ambient (W/m2) convective heat transfer rate from glass cover outer surface to ambient (W/m2 K) convective heat transfer rate within solar still from water to glass cover (W/m2) convective heat transfer rate within solar still from water to glass cover inner surface (W/m2) evaporative heat transfer from cooling film (W/m2) evaporative heat transfer rate within solar still from water to glass cover (W/m2) evaporative heat transfer rate within solar still from water to glass cover inner surface (W/m2) heat loss between packed layer and saline water (W/ m2 ) heat energy required to heat the make-up water to the basin temperature (W/m2) radiative heat transfer rate from cooling film to ambient (W/m2) radiative heat transfer rate from glass cover outer surface to surroundings (W/m2 K) radiative heat transfer rate within solar still from water to glass cover (W/m2) radiative heat transfer rate within solar still from water to glass cover inner surface (W/m2) total heat transfer rate within solar still from water to glass cover (W/m2) total heat transfer rate within solar still from water to glass cover inner surface (W/m2) rate of energy transferred from chamber-I to chamberII (W/m2) heat transfer rate between basin liner and water mass (W/m2) heat transfer rate (W) condensation heat flux (W/m2) evaporation heat flux (W/m2) solar absorption of diffuse radiation (W) solar absorption of direct radiation (W) solar absorption of reflected radiation from external reflector (W) solar absorption of reflected radiation from internal reflector (W) rate of thermal energy feed from external devices to the solar still (W/m2) coefficient of correlation reflectivity gas constant relative humidity reflectivity of wall surface Rayleigh number (¼GrPr) modified Rayleigh number Reynolds number

859

s t T Tg0 Ti Tt Tw0 Twc U Ub

salinity (g/kg) time (s) temperature (1C) initial temperature of glass cover (1C) mean operating temperature (1C) temperature at time t (1C) initial temperature of water (1C) temperature of water in evacuated tube collector (1C) overall heat loss coefficient (W/m2 K) overall bottom heat loss coefficient between water mass and atmosphere (W/m2 K) Ubs total bottom and side heat loss coefficient between water mass and ambient (W/m2 K) UL1 overall heat loss coefficient from absorber plate below PV/T module to ambient (W/m2 K) ULC overall heat transfer coefficient for collector (W/m2 K) ULET evacuated tube heat loss coefficient (W/m2 K) ULS overall heat loss coefficient between water mass and atmosphere (W/m2 K) Uss overall side heat loss coefficient between water mass and atmosphere (W/m2 K) Ut overall top heat loss coefficient between water mass and atmosphere (W/m2 K) Ut,c–a top heat loss coefficient from solar cell to ambient (W/ m2 K) Ut,gi–a overall heat loss coefficient from glass cover inner surface to atmosphere (W/m2 K) (UA)C overall heat transfer coefficient from absorbing plate of collector to ambient (W/1C) (UA)eff, UL heat loss terms (W/m2 1C) (UA)hx overall heat transfer coefficient from working fluid in heat exchanger to basin water (W/1C) (UA)p overall heat transfer coefficient from working fluid in connecting pipe to ambient (W/1C) v wind velocity (m/s) V volume (m3) VF view factor W compressor power (W) Xi theoretical or predicted value y1 instantaneous gain efficiency y2 instantaneous loss efficiency Yi experimental value Z depth of upper water column Greek

α absorptivity α0 fractional solar flux absorbed ατ product of absorptance and transmittance (ατ)eff, (ατ)EFF heat gain terms (W/m2 1C) β coefficient of volumetric expansion coefficient (1/K) βg incident angle of sun ray to glass cover ε emissivity τ transmissivity τhx fraction of energy absorbed by heat exchanger surface τwu transmissivity of upper water column θ inclination of glass cover with horizontal γ azimuth angle of the still ϕ altitude angle of the sun φ azimuth angle of the sun ρ density (kg/m3) μ viscosity (N s/m2) σ Stefan–Boltzmann constant (W/m2 K4)

860

η ηi ηiG ηiL ζ ΔT 0s Δt

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efficiency instantaneous efficiency instantaneous gain efficiency instantaneous loss efficiency vapor extraction ratio difference between inlet and outlet temperatures of saline water after recovery (1C) time interval (s)

Subscripts 1 2 a ab ac act b bk bw bm br c c1 c2 cc cd cf cf1 cf2 co cov C C1 C2 df e eff ev ex ext ET f fa fn fw g g1 g2 gi gl go gr gu

initial final air or ambient absorber aperture of concentrator activated carbon basin liner back back wall bulk-motion black rubber convective chamber-I chamber-II Chilton–Colburn conductive cooling film cooling film inlet cooling film exit condenser cover collector first collector second collector diffuse evaporative effective evaporator exit external evacuated tube humid air (or) mixture of water–vapor and air floating absorber fin material flowing water glass cover glass cover 1 glass cover 2 glass cover inner surface lower glass cover glass cover outer surface gravel upper glass cover

Solar desalination is a promising alternative that can partially support the human needs for fresh water with an environment-friendly energy source. It exhibits a considerable economic advantage over other distillation processes due to cost-free resource and reduced operation and maintenance cost. The solar desalination systems are used with a wide variety of designs, configurations, geometry, and fabrication materials. The simple and independent operation of solar distillation unit is highly suitable for small scale and remote applications. It provides an opportunity for rural communities to prepare

hx hxf in ins int j ju l m met mix ml ms out pc pcm pf pkd pl pl1 pl2 pow pt pu r r re ref rw sa si sky sl sm sp ss st s su sur sw t u v ve vg vs w wc wf wil wk wl wu

heat exchanger heat exchanger fluid inlet insulation internal 1,2,3,4…up to the order of effects jute cloth lower basin PV/T module methanol saturated mixture melting metallic sheet outlet pipe connecting collector to solar still phase change material porous fins packed layer absorber plate upper plate surface lower plate surface pond water packed bed storage tank purging radiative receiver of concentrator reflector refrigerant replacing water sand liquid interface sky side of basin wetted by lower water column storage medium suspended plate side walls of solar still in contact with water mass storage tank solar still side of basin wetted by upper water column surface of solar pond saline water total upper basin vapor vent water vapor at the condensing surface water vapor at the liquid surface water mass water in evacuated tube collector water film inlet water to flat plate collector wick material lower water column upper water column

their own potable water at considerably lower prices. Delyannis [3] provided a historical overview of solar desalination systems by highlighting the most important ideas and features developed to use solar energy for desalination of sea and brackish water. Among the available solar desalination systems, solar still is a very simple and easy to construct device that produces potable water from brackish water. It has many features, but the daily output from the solar still is not sufficient to meet the end users’ needs. Different solar still designs have been developed over the years and numerous

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

experimental as well as theoretical investigations have been carried out by the researchers to improve the performance. But the experimental research requires high investment cost and comparatively longer duration. Also it does not provide any flexibility during the analysis of influencing parameters due to complexity in fabrication and its operation. Hence the theoretical analysis is found more suitable to assess the critical parameters for the efficient operation of solar still. Thermal modeling is one of the effective methods for theoretical investigations to predict the performance of any thermal system. The thermal model of a solar still is developed based on energy balances of its components. Thermal models provide a clear understanding of the solar still behavior in actual climatic conditions. In this context, various thermal models like Dunkle’s model, Kumar and Tiwari model, Adhikari et al. model, etc. were developed and used for the analysis. Even though, all these models and various designs are not converted into real time applications due to low productivity and other operational issues. Also, no separate platform is used while considering the various parameters in the design of the solar still. Therefore, a critical analysis is required on various thermal models and various designs for clear understanding of solar still performance for commercialization of this product in rural communities. This paper aims to provide a comprehensive review on various thermal models developed for both passive and active solar stills by the researchers over the years. The effect of various design modifications in solar still with respect to theoretical model development is also reviewed in detail and also it demonstrated the new dimensions in further research. The following section provides the basics of solar still working principle to understand the science behind the separation of pure water from brackish water.

2. Solar still—A preamble Solar still is a sealed enclosure contains brackish water in its shallow basin below the air space in which water evaporation and vapor condensation are performed simultaneously. The enclosed trapezoidal structure is generally made up of materials like galvanized iron, aluminum, wood, concrete, Plexiglas, asbestos, masonry bricks, etc. The top side is covered by a glazy and highly transmitting material like glass or plastic for free flow of water droplets condensed on the surface. The inner side of the enclosure is painted black for maximum absorption of radiation energy from the sun. The entire setup is perfectly insulated at bottom as well as all four sides to reduce thermal losses from basin water to the atmosphere. Glass wool, polyurethane foam, and saw dust are some of the widely used insulating materials for the solar still. The single basin single slope solar still is the simplest design which can be fabricated at much lower cost with easily available materials. Fig. 1 shows the schematic of a simple solar still. It operates on the principle of natural hydrological cycle of evaporation and condensation of water. The evaporation process leaves behind the impurities in the basin of the enclosure and the condensation process produces pure water. The solar still receives thermal energy from the sun in the form of radiation and subsequently heats the water mass kept in the basin. Due to heating, the water gets evaporated to form water–vapor. The air–vapor mixture at the water surface has higher temperature and lower density than the air–vapor mixture near the top cover. This induces convection currents between water surface and top cover surface. The saturated air–vapor mixture rises towards upper side due to temperature and density difference and condenses partially when it is in contact with the top cover surface. The distillate is collected in a channel provided along the lower side of the cover and subsequently collected in a beaker through a rubber tube. Provisions are also made in the enclosed structure to pour brackish water into the basin and to remove the impurities formed due to evaporation of

861

Fig. 1. Schematic of a single basin single slope solar still.

water. The entire setup is kept on a stand to face South direction to receive maximum radiation energy from the sun throughout the day. The solar still can be broadly classified as Passive Solar Still (PSS) and Active Solar Still (ASS). The passive solar still utilizes the radiative energy and it is the only source to evaporate the water mass kept inside the basin. But in active solar still, additional thermal energy is fed into basin water by means of some external devices like flat plate collector, evacuated tube collector, parabolic and v-trough concentrators, solar pond, photovoltaic/thermal systems, etc. Many theoretical and experimental attempts have been made to improve its performance during last few decades. Numerous operational and design modifications have been carried out to improve its productivity by many researchers over the years. Development of thermal models provides insights into heat transfer phenomena and in turn for the improvement of solar still efficiency.

3. Need for thermal models Many research works have been reported in the literature on the experimental investigations to find a better design for solar desalination systems. Generally, the experimental researches are so costly and time consuming. Therefore, mathematical modeling may be the best alternative to find better designs and operational parameters for solar stills. Mathematical models or thermal models can be developed based on the energy balances for various components of the still. The availability of computing facilities nowadays makes the development of theoretical analysis much faster and more accurate. A solar distillation system can be efficiently designed for a given capacity by using thermal modeling without spending much cost and time. Thermal models can help to make decisions regarding shape, size, type, operating and design parameters, etc. of the distillation unit for achieving maximum distillate output under known circumstances. The simulation of thermal models will be helpful to investigate the effects of a change in certain parameters during the design stage itself. They can be simulated to any real or ideal conditions. Complex designs and the most influencing parameters that affect the productivity can be analyzed effectively. But the prediction accuracy of any thermal model is based on the clear understanding and successful formulation of its energy balance equations. The study on the effect of climatic, design and operational parameters of the solar still can be done theoretically based on certain assumptions. But the assumptions should not deviate from the real operational environment of the still. The theoretical model developed by the empirical relations must be validated through experimental data to establish its accuracy. The performance prediction of the solar still depends upon the accurate estimation of various heat and mass transfer coefficients

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between the components. Various empirical correlations have also been reported by the researchers to determine the important heat transfer coefficients involved in the desalination process. The following sections describe the basic heat transfer mechanism in solar still, energy balance equations for both passive and active solar stills, popular thermal models used by the researchers, and various modifications in the energy balance equations in detail.

4. Heat transfer mechanisms in a solar still Generally, a heat transfer process is broadly classified as being either steady or transient. During steady heat transfer process, the temperature or heat flux remains unchanged with time, but in transient process these properties are time dependent. Most of the heat transfer processes encountered in practice are transient in nature. The transient heat transfer processes are difficult to analyze, but they could be analyzed based on some presumed steady conditions. The heat transfer in a solar still is considered as the transient heat transfer process due to the variation in the temperature or heat flux with respect to time. Fig. 2 shows the energy flow that take place inside as well as outside of the single basin single slope solar still during the desalination process. 4.1. Modes of heat transfer in a solar still The heat transfer process in a solar still can be broadly classified into internal and external heat transfer processes based on energy flow in and out of the enclosed space. The internal heat transfer is responsible for the transportation of pure water in the vapor form leaving behind impurities in the basin itself, whereas the external heat transfer through the condensing cover is responsible for the condensation of pure vapor as distillate. Both these processes are briefly explained in the following sections [4]: 4.1.1. Internal heat transfer The heat exchange between water surface and glass cover inner surface of the solar still is known as internal heat transfer. There are three modes, namely convection, radiation and evaporation processes, by which the internal heat transfer process within the solar still is governed. These three modes of internal heat transfer process are described as follows: 4.1.1.1. Convection heat transfer. Convection heat transfer process is complicated in nature by the fact that it involves fluid motion as

well as heat conduction. The convection heat transfer strongly depends on fluid properties and geometry and roughness of solid surface involved. In a solar still, the convection heat transfer takes place between basin water and glass cover inner surface across humid air due to temperature difference between them. The convective heat transfer rate inside the solar still can be expressed in terms of water temperature (Tw) and glass cover inner surface temperature (Tgi) by the following relation: qc;w  gi ¼ hc;w  gi ðT w  T gi Þ

ð1Þ

In the above expression, hc,w  gi is the convective heat transfer coefficient between water mass and glass cover inner surface and can be calculated as follows:  
 ðP w  P gi ÞðT w þ273:15Þ 1=3 hc;w  gi ¼ 0:884  T w  T gi þ ð2Þ 268:9  103  P w The saturation vapor pressures at water temperature and glass cover inner surface temperature are evaluated by the following expressions:    5144 ð3Þ P w ¼ exp 25:317  T w þ 273    5144 P gi ¼ exp 25:317  T gi þ 273

ð4Þ

4.1.1.2. Radiation heat transfer. The radiation heat transfer occurs through a mechanism that involves the emission of internal energy of the object. The energy transfer by radiation is the fastest and it suffers no attenuation in a vacuum. Also, the radiation heat transfer occurs in solids as well as in liquids and gases. Even it can occur between two bodies separated by a medium which is colder than both the bodies. The radiative heat transfer occurs at inside of the solar still between water mass and glass cover inner surface. The view factor plays a major role in determining the rate of radiative heat transfer. In solar still, the view factor is assumed as unity since the inclination of glass cover with horizontal is small. The radiative heat transfer rate between water and glass cover inner surface can be obtained by the following relation
 qr;w  gi ¼ hr;w  gi T w  T gi ; ð5Þ where hr,w  gi is the radiative heat transfer coefficient between water mass and glass cover inner surface and evaluated by h
2 i
 hr;w  gi ¼ εeff σ ðT w þ 273Þ2 þ T gi þ 273 T w þ T gi þ 546 ð6Þ The effective emittance between water mass and glass cover is given as  1 1 1 εeff ¼ þ 1 ð7Þ

εw εg

4.1.1.3. Evaporation heat transfer. Evaporation occurs at the liquidvapor interface when the vapor pressure is less than the saturation pressure of the liquid at a given temperature. The evaporation heat transfer occurs in the solar still between water and water–vapor interface. The rate of evaporative heat transfer between water mass and glass cover inner surface is given by
 qe;w  gi ¼ he;w  gi T w T gi

Fig. 2. Schematic of energy flow in a single basin single slope solar still.

ð8Þ

In the above expression, he,w  gi is called as evaporative heat transfer coefficient between water mass and glass cover inner

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

The total top heat loss is the summation of convective and radiative heat losses which is given as

surface and determined by

he;w  gi ¼ 16:273  10  3  hc;w  gi



P w  P gi T w  T gi

 ð9Þ

The total internal heat transfer rate is the summation of convective, radiative, and evaporative heat transfer rates between water mass and glass cover inner surface which is given as qt;w  gi ¼ qc;w  gi þ qr;w  gi þ qe;w  gi Also,
 qt;w  gi ¼ ht;w  gi T w  T gi

 Kg
T  T go Lg gi

ð11Þ

ð12Þ

ð13Þ

4.1.2. External heat transfer The external heat transfer consists of conduction, convection, and radiation processes which are independent of each other. It is considered as the loss of heat energy from the solar still to the atmosphere. The heat lose in the solar still from glass cover outer surface to the atmosphere is called as top loss heat transfer process and from water mass to the atmosphere through insulation is called as bottom and side loss heat transfer process. The higher the former the higher will be the yield from the solar still and lower the latter better will be the yield. They are described briefly in the following section: 4.1.2.1. Top loss heat transfer. The heat energy from the glass cover outer surface is lost to the atmosphere by convection and radiation heat transfer processes. The convection heat loss from glass cover outer surface of the solar still to the atmosphere is given by
 qc;go  a ¼ hc;go  a T go  T a ð14Þ The convective heat transfer coefficient (hc,go  a) is expressed in terms of wind velocity (v) as follows: hc;go  a ¼ 2:8 þð3:0  vÞ

ð18Þ

Also,
 qt;go  a ¼ ht;go  a T go  T a

ð19Þ

The total top heat loss coefficient between glass cover outer surface and atmosphere can be obtained by the following relation:

The rate of conductive heat transfer from glass cover inner surface to the glass cover outer surface is given by qcd;gi  go ¼

qt;go  a ¼ qc;go  a þ qr;go  a

ð10Þ

The total internal heat transfer coefficient between water mass and glass cover inner surface (ht,w gi) is obtained by the following expression: ht;w  gi ¼ hc;w  gi þ hr;w  gi þ he;w  gi

863

ð15Þ

The radiation heat loss from glass cover outer surface of the solar still to the surroundings is given by
 qr;go  a ¼ hr;go  a T go  T a ð16Þ

ht;go  a ¼ hc;go  a þ hr;go  a

ð20Þ

The total top heat loss coefficient can also be determined directly in terms of wind velocity (v) by considering the effect of both radiation and free convection from the condensing cover by the following expression: ht;go  a ¼ 5:7 þ ð3:8  vÞ

ð21Þ

No significant variation is observed in the performance of the solar still by using Eq. (20) or Eq. (21). The overall heat loss coefficient from glass cover inner surface to the ambient is given as U t;gi  a ¼

ðK g =Lg Þht;go  a ðK g =Lg Þ þ ht;go  a

ð22Þ

The overall top heat loss coefficient from water mass to the atmosphere through the glass cover is expressed as Ut ¼

ht;w  gi U t;gi  a ht;w  gi þ U t;gi  a

ð23Þ

4.1.2.2. Bottom and side loss heat transfer. The heat energy is lost from water to the atmosphere through basin liner and insulation by conduction, convection and radiation processes. In case of solar still mounted on stand, the bottom and side heat losses occur in sequence—first convection, then conduction and, finally, convection and radiation losses to the ambient. But, in case of grounded solar still, the bottom heat loss is first in the form of convection and then conduction only. The rate of convective heat transfer between basin liner and the water mass is given by qw ¼ hw ðT b  T w Þ

ð24Þ

where “hw” is the convective heat transfer coefficient from basin liner to the water. The rate of conduction heat transfer between basin liner and the atmosphere is given by qb ¼ hb ðT b  T a Þ

ð25Þ

The radiative heat transfer coefficient between glass cover outer surface and the surrounding is given as " # ðT go þ 273Þ4  ðT sky þ 273Þ4 hr;go  a ¼ εg σ ð17Þ ðT go  T a Þ

The heat transfer coefficient between basin liner and the atmosphere through the insulation is

where

where

T sky ¼ T a  6

ht;b  a ¼ 5:7 þ ð3:8  vÞ

 hb ¼

Lins 1 þ K ins ht;b  a

1

ð26Þ

ð27Þ

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The overall bottom heat loss coefficient between water mass and atmosphere is given by Ub ¼

hw hb hw þ hb

ð28Þ

The overall side heat loss coefficient between water mass and atmosphere is expressed as   Ass U ss ¼ ð29Þ Ub Ab The total bottom and side heat loss coefficient from water mass to atmosphere can be given by U bs ¼ U b þ U ss

ð30Þ

For lower water depth, the overall side heat loss coefficient (Uss) can be neglected since the area of side walls losing heat (Ass) is very small compared with area of basin (Ab) of the solar still. The overall external heat loss coefficient from water mass to the atmosphere through top, bottom and sides of the solar still is expressed as U LS ¼ U t þ U bs

qe;w  gi he;w  gi  ðT w  T gi Þ  3600 ¼  3600 hfg hfg

ð32Þ

The daily yield is also calculated as M ew ¼

24 X

mew

5. Thermal analysis of solar still The single basin single slope (SBSS) solar still is the cheapest and easy to fabricate solar still compared with other designs. The analysis of SBSS will be easier to understand and the concepts developed from the investigations could be implemented on other designs. The thermal model of a single basin single slope solar still is derived by the energy balance equations of its components, namely, basin, water mass, and glass cover. The energy balance in each region of the solar still is written for the average temperature in that region. All equations are developed per unit area of the solar still components. The following session provides a basic idea to solve the energy balance equations of solar still. 5.1. Assumptions The following assumptions have been made while writing the energy balance equations:

ð31Þ

4.1.3. Calculation of yield and thermal efficiency The hourly yield from the solar still can be calculated as mew ¼

Also, the root mean square of percentage deviation (e) is expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðei Þ2 e¼ ð39Þ N

1. 2. 3. 4. 5.

There is no vapor leakage in the solar still The water mass in the solar still basin is assumed to be constant The evaporative loss of water mass is negligible The temperature gradient along water mass depth is negligible The heat capacity and absorptance of the glass cover and insulating material is negligible 6. The inclination of the glass cover with horizontal is small 7. The areas of water surface, glass cover, and basin are equal

ð33Þ

i¼1

5.2. Energy balance equations

The instantaneous thermal efficiency is expressed as

ηi ¼

qe;w  gi IðtÞs

ð34Þ

The overall thermal efficiency of passive solar still is determined by the following expression: P mew  hfg ð35Þ ηpassive ¼ P IðtÞs  As  3600 Also, the overall thermal efficiency of active solar still is given as P mew  hfg P ð36Þ ηactive ¼ P IðtÞC  AC  3600 IðtÞs  As  3600 þ

4.1.4. Accuracy of thermal models The results predicted from various thermal models can be validated through experimental data. The accuracy in prediction may be found by determining the correlation coefficient (r) and root mean square of percentage deviation (e) between the theoretical and experimental values. The correlation coefficient (r) for “N” number of observations is evaluated as
P 
P  P N XiY i  Xi Yi ffi ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð37Þ P 2
P 2 P 2
P 2 Xi Yi N Yi  N Xi  The percentage deviation (ei) is expressed as ei ¼

Xi  Y i  100 Xi

ð38Þ

The energy balance equations at various portions of the solar still are described as follows [4,5]: Glass cover outer surface Rate of energy received from glass cover inner surface by conduction ¼ Rate of energy lost to the ambient by convection and radiation

qcd;gi  go ¼ qc;go  a þ qr;go  a

ð40Þ

or qcd;gi  go ¼ qt;go  a

ð41Þ

By substituting Eqs. (13) and (19) in Eq. (41), the energy balance equation of glass cover outer surface becomes, 
 Kg
T T go ¼ ht;go  a T go  T a Lg gi

ð42Þ

The above expression is rearranged as T go ¼

ðK g =Lg ÞT gi þ ht;go  a T a ðK g =Lg Þ þht;go  a

ð43Þ

Glass cover inner surface Rate of energy absorbed from solar radiation þ Rate of energy received from water mass by convection; evaporation and radiation ¼ Rate of energy lost to the glass outer surface by conduction

α0g IðtÞs þ qc;w  gi þ qe;w  gi þqr;w  gi ¼ qcd;gi  go

ð44Þ

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

where

or

α0g IðtÞs þ qt;w  gi ¼ qcd;gi  go

ð45Þ

αeff ¼ α0b

By substituting Eqs. (11) and (13) in Eq. (45), it becomes,




α0g IðtÞs þ ht;w  gi T w  T gi ¼

 Kg
T  T go Lg gi

where
 α0g ¼ 1  Rg αg

ð47Þ

α0g IðtÞs þ ht;w  gi T w þ U t;gi  a T a ht;w  gi þ U t;gi  a

U LS ¼ U t þ U b ht;w  gi U t;gi  a Ut ¼ ht;w  gi þ U t;gi  a Ub ¼

hw hb hw þ hb

Eq. (57) is rearranged as dT w U LS α IðtÞs þ U LS T a þ T w ¼ eff dt mw C w mw C w

ð48Þ

dT w þ aT w ¼ f ðtÞ dt

a¼

Rate of energy absorbed from solar radiation

U LS mw C w

¼ Rate of energy lost to water mass by convection f ðtÞ ¼

þ Rate of energy lost to the ambient by conduction and convection

α0b IðtÞs ¼ qw þ qb

ð60Þ

¼ hw ðT b  T w Þ þ hb ðT b  T a Þ

ð62Þ

1. The time interval Δt (0 o toΔt) is small. 2. The value of “a” is constant during the time interval Δt. 3. The function “f(t)” is constant for the time interval between 0 and t, i.e. f ðtÞ ¼ f ðtÞ.

ð51Þ

ð52Þ

hw þ hb

mw C w

ð50Þ

Eq. (50) can be rearranged as

α0b IðtÞs þ hw T w þ hb T a

αeff IðtÞs þ U LS T a

The following assumptions have been made to find the approximate analytical solution for the above equation:

where

α0b ¼ αb ð1  αg Þð1  Rg Þð1 Rw Þð1  αw Þ

ð61Þ

ð49Þ

By substituting Eqs. (24) and (25) in Eq. (49), it becomes,

Tb ¼

ð59Þ

where

Basin liner

0 b IðtÞs

ð58Þ

Eq. (59) can be expressed in simplified form as follows:

Rearranging the above equation, we get, T gi ¼

ht;w  gi hw þ α0w þ α0g hw þ hb ht;w  gi þ U t;go  a

and ð46Þ

Eq. (46) can be rewritten as follows by substituting the value of Tgo, !

 ht;go  a T gi ht;go  a T a
 α0g IðtÞs þ ht;w  gi T w  T gi ¼ K g =Lg K g =Lg þ ht;go  a

α

865

By using the boundary condition, T wðt ¼ 0Þ ¼ T w0 , the solution for above first order differential equation is Tw ¼

f ðtÞ 1  e  at þ T w0 e  at a

ð63Þ

Water mass Rate of energy absorbed from solar radiation 6. Well-liked thermal models

þ Rate of energy received from basin liner by convection þ Rate of energy received from external devices ¼ Rate of energy stored þ Rate of energy lost to the glass inner surface by convection; evaporation and radiation

α0w IðtÞs þ qw þ Q u ¼ mw C w

dT w þ qc;w  gi þ qe;w  gi þ qr;w  gi dt

ð53Þ

(Or)

α

0 w IðtÞs þ qw þ Q u

The variety of research on solar still energy analysis is well used for the improvement of system performance. Many thermal models were developed by the scientists based on the solar still dependent and independent variables. The following section briefly describes the well-known thermal models developed by various researchers over the years for the prediction of solar still performance and also provides its limitations. 6.1. Dunkle’s model [1961]

dT w þ qt;w  gi ¼ mw C w dt

ð54Þ

Substituting Eqs. (24) and (11) in Eq. (54), it becomes,

α0w IðtÞs þ hw ðT b  T w Þ þ Q u ¼ mw C w


 dT w þ ht;w  gi T w  T gi dt

where

 α0w ¼ 1  αg 1  Rg ð1  Rw Þαw

ð55Þ

ð56Þ

For passive solar still, Q u ¼ 0 Eq. (55) can be simplified by substituting the values of Tb and Tgi and given as

αeff IðtÞs þ U LS T a ¼ mw C w

dT w þ U LS T w dt

ð57Þ

Dunkle’s model is the most popular model to evaluate various heat transfer coefficients involved in a solar still. It provides widely accepted empirical correlations to predict the performance of the single effect solar still. Dunkle used the following Nusselt–Rayleigh empirical correlation developed by Jakob [1957] for free convection of air in an enclosure: Nu ¼ C U Ran with C ¼ 0:075 and n ¼ 1=3

ð64Þ

Dunkle estimated the value of he,w  g by using the following relations:   P w  P gi ð65Þ he;w  g ¼ 0:0163  hc;w  g T w  T gi

866

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911



1=3 hc;w  g ¼ 0:884  ΔT 0 where  
 ðP  P ÞðT þ 273:15Þ ΔT 0 ¼ T w  T gi þ w gi w 3 268:9  10  P w

ð66Þ




ð67Þ

1. The free convection in the still described by the above correlations was originally developed for free convection of air without evaporation. 2. The thermo physical properties of moist air are taken for mean operating temperature of water at Tw E50 1C. 3. The equivalent range of temperature difference between evaporation and condensation surfaces is considered as 17 1C. 4. The evaporative and condensing surfaces are considered as parallel. 5. The ignorance of characteristic length between evaporative and condensing surfaces. It has been observed that the Dunkle’s model has been used by most of the researchers in the field of solar distillation even in the conditions that are not falling under the limitation of the model. 6.2. Chen et al.’s model [1984] Chen et al. have proposed a model to evaluate the convective heat transfer coefficient based on a wide range of Rayleigh number (3.5  103 o Ra o1  106) which is given as, Kf df



ΔT 0 ¼ T w  T g þ

The major drawbacks of the Dunkle’s model are:

hc;w  g ¼ 0:2Ra0:26

where

ð68Þ

n ¼ 1=3 for 2:51  105 o Gr o 107 n ¼ 1=4 for 104 o Gr o2:51  105

6.5. Kumar and Tiwari model [1996] Kumar and Tiwari have developed a theoretical model to evaluate internal heat transfer coefficients based on linear regression analysis using experimental data. The model could be more realistically used for wide range of water temperature and the values of constants C and n are not fixed as in the case of other models. They evaluated the constants C and n used in determination of non-dimensional Nusselt number which is related to convective heat transfer coefficient. The effects of solar still cavity, operating temperature range and orientation of condenser cover have been taken into account during the development of this model. The Nusselt number for convective heat transfer coefficient can be expressed as follows: Nu ¼

Clark proposed a model which is similar to Dunkle’s model to evaluate the rate of evaporative heat transfer using the rate of evaporative mass flux in an air–water mixture humidification process.
0 
 qe;w  g ¼ k =2 hc;w  g P w  P gi ð69Þ

or

0

1. Spacing between evaporating and condensing surfaces is large. 2. Rate of evaporation and condensation are equal, which is only possible for a high operating temperature range (4 80 1C) of the distillation system. Clark has validated the model experimentally for the operating temperature range greater than 55 1C. The experiment was conducted in an air conditioned room which provides large heat transfer from the glass cover to the room ambient. But this is normally not the situation in real operating condition of the solar still under natural climatic conditions. 6.4. Adhikari et al.’s model [1990] Adhikari et al. argued that the Dunkle’s relation is valid only when the Grashof number is less than 2.51  105 and needs to be modified for higher values of the Grashof number. They performed a simulation experiment to evaluate the amount of water evaporated in a solar still under steady state conditions in a controlled environment. They suggested the following relation to estimate the hourly distillate yield directly such as,
n
 mew ¼ α ΔT 0 P w P gi ð70Þ

ð71Þ

268:9  103  P w

The value of α is a constant for a particular operating range of a solar still. If the operating temperature range is changed, then a different value of α is required for the estimation of hourly yield. Table 1 gives the value of α for different water temperature of the solar still and for different Grashof numbers. The values of constants used in the above expression are calculated based on Grashof number and water temperature as follows:

6.3. Clark’s model [1990]

where k ¼ 0:016273. The above equation is generally valid when

ðP w  P g ÞðT w þ 273:15Þ

hc;w  g df ¼ CðGrPrÞn Kf

ð72Þ

Kf CðGrPrÞn df

ð73Þ

βgdf 3 ρ2f ðT w  T gi Þ μ2f

ð74Þ

hc;w  g ¼ where Gr ¼

Pr ¼

μf C pf

ð75Þ

Kf

The distillate output from evaporation surface during time “t” can be expressed as follows: mew ¼


 0:01623 K f   CðGrPrÞn  P w  P gi  Ab  t hfg df

ð76Þ

The constants C and n are determined from experimental data by using the following relations: C ¼ expðC 0 Þ n¼m Table 1 Values of α for different water temperatures and Grashof numbers. Water temperature (1C)

α  109 Gro 2.51  105

Gr 42.51  105

40 60 80

8.1202 8.1518 8.1895

9.7798 9.6707 9.4936

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

where 

Σ

C0 ¼

N i ¼ 1 yi



Σ







 Σ Σ  2 N N N Σ i ¼ 1 x2i  Σ i ¼ 1 xi 

N 2 i ¼ 1 xi

N i ¼ 1 xi

N i ¼ 1 xi yi

7.1. Single basin single slope passive solar still



   N N N N Σ i ¼ 1 xi yi  Σ i ¼ 1 xi Σ i ¼ 1 yi m¼   2 N N N Σ i ¼ 1 x2i  Σ i ¼ 1 xi

867

ð77Þ

ð78Þ

In the above correlations, N is the appropriate value of observations, and “x” and “y” values are taken from experimental data.

Numerous research works have been reported on the development of theoretical models for single basin single slope solar passive stills in the past few decades. The schematic of the passive solar still was already shown in Fig. 1. The passive solar still only utilizes the direct solar energy falling on it and no external device is augmented to supply additional thermal energy to the basin water. Therefore, the following expression is valid for the energy balance of water mass in the passive solar still: Qu ¼ 0

6.6. Zheng Hongfei et al.’s model [2001] Zheng et al. made a little modification in the expression proposed by Chen et al. model to determine internal convective heat transfer coefficient which is given by:
0:26 K f hc;w  g ¼ 0:2 R0a df

ð79Þ

where df ρf g β 3

R0a ¼

μf αf

and

ΔT″ ¼

ΔT″

 
 ðP w P gi ÞðT w þ 273:15Þ T w  T gi þ ððM a P t Þ=ðM a  M w ÞÞ  P w

ð80Þ

ð81Þ

In the above expression (80), “αf” represents the thermal diffusivity of humid air. 6.7. Tsilingiris model [2007] Tsilingiris proposed a refined model to describe simple procedures for the first order evaluation of the thermo-physical properties of humid air, based on dry air and water–vapor properties. He used the thermo-physical properties of binary mixture of dry air and water–vapor instead of improper dry air properties alone to predict the convective and evaporative heat transfer coefficients as well as the distillate productivity in solar distillation systems. The convective heat transfer coefficient is expressed as   n  T ðP vs P vg ÞðM a  M v Þ n g ρmix β hc;w  g ¼ CK mix ðT si  T g Þ þ si M a P t  P vs ðM a M v Þ μmix dmix ð82Þ The evaporative heat transfer coefficient is given by hc;w  g ðRc Þa Pt he;w  g ¼ 1000hfg C p;a ðRc Þv ðP t  P vs ÞðP t  P vg Þ

7.1.1. Jute cloth Sakthivel et al. [6] developed a mathematical model to improve the efficiency of the solar still with jute cloth as a medium which provides large evaporation surface. The proposed system utilizes the latent heat of condensation accumulated in the space between the saline water and the glass cover. The jute cloth was kept in vertical position in the middle of the basin saline water and another row of jute cloth was attached with the rear wall of the passive solar still as shown in Fig. 3. The bottom edge of the jute cloth was dipped into the basin saline water. While most of the incident solar radiation was absorbed by the basin, portion of radiation was absorbed by the jute cloth. It provides more evaporation surface and as the heat capacity of the jute cloth is low, it can attain high temperature. The Dunkle’s model was used to evaluate the convective and evaporative heat transfer coefficients between jute cloth and glass cover inner surface to determine the hourly yield rate by measuring the temperature of the jute cloth (Tju), as follows: The convection heat transfer from jute cloth to glass cover inner surface is given as qc;ju  gi ¼ hc;ju  gi ðT ju  T gi Þ

ð85Þ

where " hc;ju  gi ¼ 0:884 


 ðP ju  P gi ÞðT ju þ 273:15Þ T ju  T gi þ 268:9  103  P ju

#1=3

The evaporation heat transfer from jute cloth to glass cover inner surface is given as qe;ju  gi ¼ he;ju  gi ðT ju  T gi Þ

ð83Þ

The condensed water mass per unit still area and time is given by   h P t ðP vs  P vg Þ ðR Þ _ w ¼ c;w  g c a ð84Þ m C p;a ðRc Þv ðP t P vs ÞðP t P vg Þ

7. Various designs of solar still and their effect on thermal models Based on the basic structure of the solar still, many design modifications were invented to improve its performance. This section categorizes various theoretical and experimental investigations carried out on the single basin single slope solar stills as well as new designs invented by the researchers over the years. The corresponding changes in their energy balances are also incorporated in the thermal model of the simple solar still.

ð86Þ

Fig. 3. Schematic of a single slope solar still with vertical jute cloth [6].

ð87Þ

868

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

where he;ju  gi ¼ 16:273  10  3  hc;ju  gi



P ju  P gi T ju  T gi

 ð88Þ

The hourly yield rate from jute cloth alone is determined by mew;ju ¼

he;ju  gi ðT ju  T gi Þ  3600 hfg

ð89Þ

The above calculated yield was added with the hourly yield of passive solar still to get the theoretical total yield rate as follows: mt ¼ mew þ mew;ju

ð90Þ

In the above model, only convective and evaporative heat transfer coefficients between jute cloth and glass cover inner surface were considered for the analysis. From the experimental study, it was found that the still daily yield with the jute cloth increases about 20% and the maximum efficiency is about 52% which is 8% higher than the conventional still efficiency. It was inferred that 30 kg of saline water in the basin is the optimized quantity to give maximum daily yield. Also, the experimental and theoretical values of hourly yield for the regenerative still fairly agree with 9% deviation. Srivastava and Agrawal [7] proposed a thermal model to analyze the performance of basin type solar still by incorporating multiple low thermal inertia porous absorbers (blackened jute cloth), floating adjacent to each other on the basin water with the help of thermocol insulation. Nine such absorber pieces were floated side by side lengthwise on the basin water so that the water surface was completely covered by the absorber with required clearance from the basin walls. The edges of the jute cloth were dipped in the basin water, so that, it remained wet due to capillary action. The performance of the modified still was compared with the perfectly synchronized conventional basin type solar still of identical dimensions and material. The effect of basin water depth and the improvement in productivity by the use of twin reflector booster were also experimentally investigated. The energy balance in various components of the modified still is shown in Fig. 4. Energy balance for the solar still:

αg IðtÞs þ τg IðtÞs ¼ qr;g  a þ qc;g  a þ qb þ C w

dT w dt

ð91Þ

Energy balance for the glass cover:

αg IðtÞs þ qr;fa  g þqc;fa  g þ qe;fa  g ¼ qr;g  a þ qc;g  a

ð92Þ

Energy balance for the floating absorber:

αfa τg IðtÞs ¼ qr;fa  g þ qc;fa  g þ qe;fa  g þ qc;fa  w

ð93Þ

Energy balance for the basin water: dT w dt

Fig. 4. Energy balance in the modified still [7].

insulation has a significant effect on the distillate output and the productivity decreases with the increase in the value of the heat transfer coefficient of floating insulation. But the basin water depth does not have any significant effect on the still productivity and it is only effective at smaller water depths. Hence it is suggested that the modification can be effectively applied on deep basin stills. 7.1.2. Deep basin Aboul-Enein et al. [8] presented a transient mathematical model for a single basin solar still with deep basin. The thermal performance of the still was investigated both experimentally and theoretically. The influence of cover slope on daily productivity and effect of heat capacity of basin water on the daylight and overnight productivities were also studied. The schematic of the deep basin solar still is shown in Fig. 5. A computer program was prepared for the solution of the energy balance equations of the still and the input parameters to the program include climatic, design and operational parameters. The following energy balance equations have been used for the still components: For the basin liner IðtÞs τg τw αb Ab ¼ hw Ab ðT b  T w Þ þU b Ab ðT b  T a Þ

ð96Þ

For the basin water IðtÞs τg αw Aw þ hw Ab ðT b  T w Þ ¼ M w C w

dT w þ ht;w  g Aw ðT w  T g Þ þ U ss Ass ðT w  T a Þ dt

ð97Þ For the glass cover IðtÞs αg Ag þ ht;w  g Aw ðT w  T g Þ ¼ hr;g  sky Ag ðT g  T sky Þ þ hc;g  a Ag ðT g  T a Þ

ð94Þ

ð98Þ

In the above equations, the radiative (qr,fa g), convective (qc,fa g) and evaporative (qe,fa g) heat transfers between the floating absorber and the glass cover are calculated by Dunkle’s model. The heat transferred from the floating absorber to the basin water is given as,

From the transient analysis, the optimum tilt angles of the solar still cover were found to be 101 during summer season and 501 during winter season in Tanta (301470 N), Egypt. The optimum insulation thickness was found to be 0.075 m for higher yield rates. It was inferred that the daylight productivity decreases with an increase of water depth and reverse is the case for overnight productivity due to the increased heat capacity of basin water with increasing depth. Also the model overestimated the daily average values of water, glass cover and basin temperatures by about 10%, 6%, and 15%, respectively.

qc;fa  w ¼ qb þ C w

qc;fa  w ¼ hc;fa  w ðT fa  T w Þ

ð95Þ

Due to low thermal inertia of the porous absorber, quicker start-up times, as well as higher operating temperatures were achieved resulting in higher distillate yield. The results indicated that about 68% more distillate output was obtained by the modified still than the conventional still on clear days whereas it was 35% on partially clear days. Also the application of twin reflector booster on the modified still gave a distillate gain of 79% over the modified still without booster. It was found that the values of the glass cover temperature, absorber temperature and distillate outputs obtained theoretically from the thermal model had fair agreement with the experimental values. It was inferred that the heat transfer coefficient of the floating

7.1.3. Double glass cover El-Bahi and Inan [9] conducted theoretical and experimental analyses for a parallel double glass solar still. A separate condenser was integrated to the evaporator of the solar still through a horizontal slot, and the upper cover was inclined for easy dropping of condensed droplets to the base of the condenser. A vertical reflector was added to increase the incident solar radiation on the

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

869

Water mass (w): mw C w

dT w ¼ IðtÞs α0w þ qw þ mwf C wf ðT wf;ex  T wf;in Þ  qr;w  g1  qc;w  g1  qe;w  g1 dt

ð106Þ Lower glass (g1): mg C g

dT g1 ¼ IðtÞs α0g1 þ qr;w  g1 þ qc;w  g1 þ qe;w  g1  qc;g1  wf  qr;g1  g2 dt ð107Þ

Water film (wf): mwf C wf

evaporator and also to make a shadow on the condenser as shown in Fig. 6. A theoretical analysis based on the energy balance for different components of the solar still was performed. The Dunkle’s relations were used to calculate the heat and mass transfer in the humid air inside the evaporator and the condenser. The energy balance equations for the various components are given below: Water mass: dT w þ ht;w  g1 ðT w  T g1 Þ þ ht;w  co ðT w  T co Þ dt

ð99Þ

Lower glass cover: ht;w  g1 ðT w  T g1 Þ ¼ ht;g1  g2 ðT g1  T g2 Þ

ð100Þ

Upper glass cover: ht;g1  g2 ðT g1  T g2 Þ ¼ ht;g2  a ðT g2  T a Þ

ð101Þ

Condenser cover: ht;w  co ðT w  T co Þ ¼ ht;co  a ðT co  T a Þ

ð102Þ

Basin liner:

τ τ

2 g w IðtÞs

¼ hw ðT b T w Þ þ hb ðT b T a Þ

The hourly rate of distillate output is given by

he;w  g1 ðT w  T g1 Þ þ he;w  co ðT w  T co Þ  3600 mew ¼ hfg

dT b ¼ IðtÞs α0b  qb  qloss dt

mg C g

dT g2 ¼ IðtÞs α0g2 þ qr;w  g2 þ qc;w  g2  qr;g2  a  qc;g2  a dt

ð109Þ

The condensation rate is calculated as follows: dmew he;w  g1 ðT w  T g1 Þ ¼ dt hfg

ð110Þ

The simulations were carried out by assuming the inlet temperature of the cooling water flowing between the double-glass cover as constant at 25 1C. It was found that the double-glass cover solar still with water cooling provided about 34% increase in productivity compared with the conventional solar still. But, perfect insulation of solar stills increased the water temperature by 67% and 32% for conventional and double glass stills, respectively. Also the parametric assessments of the double-glass solar still showed that the effects of cooling water flow rate and the glass spacing on productivity were small. 7.1.4. Double condensing chamber Aggarwal and Tiwari [11] presented a thermal model for double condensing chamber solar still. The upward heat loss was reduced by using double glazing. The chamber-II was created behind the partition wall using stainless steel as condensing cover-II. It was

ð103Þ

ð104Þ

The proposed system minimized the formation of water droplets on the inner surface of the inner glass, which are responsible for reflecting/absorbing some of the incident radiation. The two glass covers decreased the heat losses by convection to the ambient, resulting in higher basin water temperature. The heat capacity of the evaporator was minimized due to small evaporator volume; consequently the system responded to solar radiation in shorter time. It was concluded that the productivity is in good agreement with the results obtained and the efficiency is increased from 48% to more than 70%, when the condenser cover was cooled down by the flowing water. Mousa Abu-Arabi et al. [10] investigated the thermal performance of a single basin solar still with double glass cover cooling. The brine water is made to flow between the double-glass arrangement to lower the glass temperature and thus increase the water-to-glass temperature difference. The arrangement is shown in Fig. 7. The numerical simulations were conducted to study the theoretical performance of the modified still. The energy balance equations for basin, water mass, lower glass cover, water film, and upper glass cover are given as follows: Basin (b): mb C b

ð108Þ

Upper glass (g2):

Fig. 5. Schematic of deep basin solar still [8].

τ2g αw IðtÞs þ hw ðT b  T w Þ ¼ mw C w

dT wf ¼ qc;g1  wf  qc;wf  g2 dt

Fig. 6. Schematic of parallel double glass solar still with separate condenser [9].

ð105Þ Fig. 7. Schematic of the double glass solar still [10].

870

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

exposed to the ambient, which helps in fast release of the latent heat of condensation. Vapor was transferred from chamber-I to chamber-II through a vent which is provided at the top of the partition wall. The diffusion of the vapors has been considered in the thermal modeling by using the diffusion coefficient. Fig. 8 shows the cross sectional view of the modified solar still. The energy balance equations are described as follows: Basin liner:

α0b IðtÞs ¼ hw ðT b  T w Þ þ hb ðT b  T a Þ

ð111Þ

Water mass: hw ðT b  T w Þ þ α0w IðtÞs ¼ mw C w ðdT w =dtÞ þ qt;w  g þ qu;c1  c2

ð112Þ

The thickness of water layer (Δy) is calculated from the following criterion: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Kw Δyr ð120Þ ðρw C w =ΔtÞ  U b Ab The energy balance equations were integrated in the time and space domains using the finite difference technique. The selected time interval (Δt) was taken as 2 min during the program execution. It was found that by using the floating aluminum perforated black plate in the solar still increases the productivity by 15% for a water depth of 3 cm and 40% for a water depth of 6 cm. Also the results of the mathematical model were in good agreement with those of the experimental model.

Inner glass (Condensing cover 1): qt;w  g ¼ ht;g1  g2 ðT g1  T g2 Þ

ð113Þ

Outer glass: ht;g1  g2 ðT g1  T g2 Þ ¼ ht;g2  a ðT g2  T a Þ

ð114Þ

Second condensing cover (Metallic sheet): qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qu;c1  c2 ¼ C diff Av =Ams 2ðdP=ρÞ U dP ¼ hc;c2  a ðT ms  T a Þ

ð115Þ

The rate of distillate output from both chambers can be obtained by using the following expressions: mew;c1 ¼ Ab he;w  g

ðT w  T g Þ hfg

ð116Þ



IðtÞs αg Ag þ ht;wu  g Awu ðT wu  T g Þ ¼ hr;g  a ðT g  T a Þ þ hc;g  a ðT g  T a Þ Ag

and mew;c2 ¼ Ams

qu;c1  c2 hfg

Suspended plate:

7.1.5. Floating perforated black plate Safwat Nafey et al. [12] developed a mathematical model to calculate the theoretical productivity of the solar still with a floating perforated black plate. A black painted aluminium sheet of thickness 0.5 mm was made floating on the brine surface by stacking five floating balls under side surface of the plate. The floating black plate allows only a thin layer of saline water to be formed above the plate surface. This layer was heated rapidly by the absorbed energy and hence the rate of evaporation was increased. Also the floating black plate decreased the heat loss to the walls and the bottom due to lowering the water temperature below the plate. They used the energy balance equations for moist air, water liner above the black plate, floating black plate, and top, nth and bottom layers of the water block in addition to the glass cover and basin liner. The values obtained from the theoretical model were compared with the experimental results. The energy balance for the floating black plate are given as

0:5IðtÞs α0pl þ

ð121Þ

ð117Þ

The theoretical and experimental values of water and glass temperatures, and distillate output were determined from the analysis. It was found that the double condensing chamber solar still gave about 46% higher output than the single slope conventional solar still. There is a fair agreement between experimental and theoretical results obtained from the model.

K pl ðT  T pl2 Þ Lpl pl1

ð118Þ


 K pl
T  T pl2 ¼ hc;pl2  wl T pl2  T wl Lpl pl1

ð119Þ

0:5IðtÞs α0pl ¼ hc;pl1  wu ðT pl1  T wu Þ þ

7.1.6. Suspended absorber El-Sebaii et al. [13] presented a transient mathematical model for a single slope single basin solar still with baffle suspended absorber. A movable suspended absorber plate was placed inside the basin water of the solar still as shown in Fig. 9. The suspended absorber divided the basin water into two portions, viz. the upper and lower water columns. The upper and lower water columns could be made contact through the vents drilled in the baffle absorber. The heat-transfer from the upper to the lower water columns and/or vice versa took place by conduction through the plate and by convection through the vents. The energy balance equations have been written for glass cover, baffle suspended plate, upper water column, and lower water column as follows: Glass cover:

IðtÞs τg τwu αpl Apv ¼ hc;pl  wu Apv ðT pl  T wu Þ þhc;pl  wl Apv ðT pl  T wl Þ ð122Þ Upper water column: IðtÞs τg αwu Awu þ hc;pl  wu Apv ðT pl  T wu Þ   Apv K pl ðT wu T wl Þ ¼ hc;wu  g Awu ðT wu  T g Þ þ Ave hc;wu  wl þ Lpl   dT wu ð123Þ þ Asu U su ðT wu  T a Þ þ M wu C w dt Lower water column:   Apv K pl ðT wu T wl Þ þ hc;pl  wl Apv ðT pl  T wl Þ IðtÞs τ g τ wu αwl Ave þ Ave hc;wu  wl þ Lpl

Fig. 8. Cross sectional view of double condensing chamber solar still [11].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

¼ ðU b Awl þ U sl Asl ÞðT wl  T a Þ þ M wl C w

  dT wl dt

ð124Þ

In the above expressions, Apv ¼Apl  Ave. The temperature of the suspended absorber plate is found from the following relation: T pl ¼

αpl τg τwu IðtÞs þ hc;pl  wu T wu þ hc;pl  wl T wl hc;pl  wu þ hc;pl  wl

ð125Þ

The energy balance equations for various parts of the still were solved analytically using the method of Gauss elimination. The theoretical model was validated with the experimental results. It was inferred that adding a suspended plate within the basin water of a conventional still decreases the preheating time required for evaporating the still water. The daily productivity of the modified still was around 18.5–20% higher than that of the conventional still. The optimum position of the baffle absorber was found to be in the middle of the basin water and with the lowest mass of the upper water with and without vents. Also it was advisable to use the suspended absorber without vents in order to obtain maximum performance. It was concluded that the developed mathematical model overestimated the daily productivity of the still only by about 8%. El-Sebaii et al. [14] made an another attempt to investigate the effect of thermal conductivity of the suspended absorber on the daily productivity of the solar still using aluminium, copper, stainless steel and mica plates as suspended absorbers. The construction of the modified still is similar to the diagram shown in Fig. 9. Also the energy balance equations for glass cover, suspended plate, upper water column and lower water column are same as used in [13]. The effect of thickness of the suspended absorber on the productivity as well as the year round performance of the solar still was studied by computer simulation for the solution of energy balance equations of the solar still. It was found that the daily productivity of the modified solar still with mica as the suspended absorber increased by about 42% higher than the conventional solar still. Also the annual average productivities of the modified still with mica were found to be 23% and 15.8% higher than those of the conventional solar still when the basin water masses were 80 kg and 40 kg, respectively. It was observed that the productivity of the modified still was less dependent on the thickness of the suspended plate and the suspended plate became more effective at higher mass of basin water. 7.1.7. Fins, sponges and wicks Velmurugan et al. [15] presented energy balance equations for single basin solar still integrated with fins, sponges and wicks. The basin plate of the conventional still was redesigned with fins of five numbers to increase the exposure area as shown in Fig. 10. The

Fig. 9. Schematic diagram of single slope single basin solar still with baffle suspended absorber [13].

871

performance was compared by means of usage of sponges. The governing energy balance equations were solved analytically and compared with the experimental results. The energy balance equation for basin, saline water and glass cover can be written as follows: Basin: IðtÞs Ab αb ¼ M b C b ðdT b =dtÞ þ Q w þ Q loss

ð126Þ

Saline water: IðtÞs Aw αw þ Q w ¼ Q c;w  g þQ r;w  g þ Q e;w  g þ M w C sw ðdT w =dtÞ

ð127Þ

Glass cover: IðtÞs Ag αg þ Q c;w  g þ Q r;w  g þ Q e;w  g ¼ Q r;g  sky þ M g C g ðdT g =dtÞ ð128Þ The specific heat of saline water (Csw) in terms of saline water temperature and its salinity is calculated by the following relation: C sw ¼ a1 þa2 T w þ a3 T 2w þa4 T 3w

ð129Þ

The constants a1, a2, a3 and a4 are calculated from a1 ¼ 4206:8  6:6197s þ 1:2288  10  2 s2

ð130Þ

a2 ¼  1:1262 þ 5:4178  10  2 s 2:2719  10  4 s2

ð131Þ

a3 ¼ 1:2026  10  2  5:5366  10  4 s þ 1:8906  10  6 s2

ð132Þ

a4 ¼ 6:8774  10  7 þ 1:517  10  6 s  4:4268  10  9 s2

ð133Þ

where “s” is the salinity of the water. Initially, the time interval was assumed as 5 s and water temperature, glass temperature and basin temperature were taken as ambient temperature during simulation. The change in basin temperature (dTb), increase in saline water temperature (dTw) and glass temperature (dTg) were computed by solving the corresponding energy balance equations. For evaluating the change in temperatures, the experimentally measured values of solar radiation and ambient temperature of the corresponding day and hour were used. The total condensation rate was given as, dmew hc;w  g ðT w  T g Þ ¼ hfg dt

ð134Þ

For the next time step, the parameter is redefined as T w ¼ T w þ dT w ;

T g ¼ T g þdT g

and

T b ¼ T b þdT b

During the experimental study, the productivity increased by about 15.3% when sponges were used. The maximum deviation between theoretical and experimental results was 10.1% for still only whereas it was less than 6.2% for sponge integrated still. About 29.6% of productivity increased when wicks were used in the still and the deviation between theoretical and experimental results was about 10.8%. But the productivity increased by around 45.5% when fins were used at the bottom of the still. The maximum deviation of the theoretical performance was 9.2% in comparison with that of the experimental. The experimental results showed that the average daily productivity was higher when fins were used in the still. Srivastava and Agrawal [16] conducted an experimental study to analyze the seasonal performance in winter and summer of a modified basin type solar still, integrated with porous fins. The effect of the basin water depth was also experimentally investigated. The experimental observations were verified with the theoretical results obtained from the thermal model for internal heat transfer based on Dunkle’s relations. In the modified still, shown in Fig. 11, thin bamboo sticks were fitted horizontally running lengthwise and widthwise crossing each other above the still base. Blackened cotton cloth or rags were suspended from the sticks, such that the lower parts of the fins were dipped in the basin water, whereas the rest of the upper

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obtained whereas it was 23% higher in the month of May. Due to good insulation property of the polystyrene foam as high as 7.5 kg/ m2 was obtained from the modified still in the month of May, when the distillate output from the conventional still was 6.5 kg/m2. Nocturnal output was also achieved from the modified still, which was marginally less than that of the conventional still. Also there is a fair agreement between the theoretical and experimental values of the distillate output.

Fig. 10. Cross sectional view of basin type solar still integrated with fins [15].

parts were extended above the basin water surface. The spacing between the porous fins was kept in such a way that there was minimum shading of the extended part of the fins by adjacent fins. The convective heat transfer between the porous fins and glass cover is given as qc;pf  g ¼ hc;pf  g ðT pf  T g Þ

ð135Þ

The convective heat transfer coefficient between the porous fins and glass cover is given as " #1=3
 ðP pf  P g ÞðT pf þ 273:15Þ ð136Þ hc;pf  g ¼ 0:884  T pf  T g þ 268:9  103  P pf The evaporative heat transfer between wet porous fins and glass cover is given by qe;pf  g ¼ he;pf  g ðT pf  T g Þ

ð137Þ

The evaporative heat transfer coefficient between the wet porous fins and glass cover is given by   P pf  P g ð138Þ he;pf  g ¼ 16:273  10  3  hc;pf  g T pf  T g The radiative heat transfer between the porous fins and glass cover is given by qr;pf  g ¼ hr;pf  g ðT pf T g Þ

ð139Þ

The radiative heat transfer coefficient between the porous fins and glass cover is given by hr;pf  g ¼ εpf F σ ðT 4pf  T 4g Þ

ð140Þ

The hourly yield rate for the porous fins is determined by mew;pf ¼

he;pf  g ðT pf  T g Þ  3600 hfg

ð141Þ

The above calculated yield was added with the hourly yield of passive solar still to get the theoretical total yield rate as follows: mt ¼ mew þ r pf mew;pf

7.1.8. Vacuum The effect of applying vacuum inside the solar still on its productivity was studied by Al-Hussaini and Smith [17]. The vacuum inside the solar still makes the convection heat transfer coefficient as zero. A steady state heat transfer through the glass was assumed by the authors at the glass cover without any appreciable error. The evaporative heat transfer coefficient is given as he;w  g ¼ 16:276  10  3 R1 " 0:884T w  T g þ

R1 ðT w  T g ÞðT w þ 273Þ 268:9  10  3  R2  R1 ðT w þ 273Þ

ð143Þ where R1 and R2 are constants. The energy balance for water mass is given as mw C w

dT w ¼ αw IðtÞs  ht;w  g ðT w  T g Þ dt

ð144Þ

The energy balance for the glass cover is given as mg C g

dT g ¼ αg IðtÞs þht;w  g ðT w  T g Þ  ht;g  a ðT g  T a Þ dt

ð145Þ

In case of vacuum, the rate of evaporation (w) is given by ð146Þ w ¼ 5:83  102 P v ðMo=TÞ1=2 f But Eq. (146) gave a high amount of water evaporation which was found not equal to the rate of condensation using the thermal balance equation at the glass cover. This is due to the fact that the glass cover was considered as a thermal resistance to the heat transfer between the vapor region and the internal surfaces of the glass cover so that the condensation process was prevented, and hence, the rate of condensation would not be equal to the rate of evaporation. So, the analysis in the case of vacuum was done by using the thermal balance of the glass cover. Therefore, the evaporative heat transfer coefficient was determined by assuming uniform glass cover temperature (Tg) with the

ð142Þ

where “rpf” is the ratio of the effective evaporation surface area of the porous fins and the basin area of the solar still. It was observed from the experimental study that, the porous fin —glass cover temperature difference is always positive, even in the morning hours when the basin water temperature is lower than the cover temperature. This corresponds to the fact that the fin type still starts producing in the morning hours, because the vertically extended fins start receiving the solar radiation and due to their low thermal inertia, evaporation starts rapidly. During the low intensity and off-sunshine period, the distillate production is supplemented from the relatively warm basin water, thus a reasonable nocturnal production is also obtained. It was found that, for the 24 h duration in the month of February, 48% higher yield was obtained, whereas it was 15% higher in the month of May. Similarly for day time in the month of February, 56% higher distillate output was

#1=3

Fig. 11. Construction of the modified solar still [16].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

following relation: ðhr;w  g þ he;w  g ÞðT w  T g Þ ¼ ht;g  a ðT g  T a Þ

ð147Þ

It was found that the enhancement of water productivity per day was more than 100% when using vacuum inside the solar still. It was inferred that the existence of non-condensable gas (such as air) adjacent to the condensate surface behaves as a thermal barrier to the heat transfer. The authors argued that the enhancement was due to the absence of convection heat transfer loss from the water and also the absence of non-condensable gases inside the still when complete vacuum was applied. 7.1.9. External condenser Mohamad Abu-Qudais et al. [18] presented a theoretical model for external condenser type solar still to predict the efficiency. The productivity and efficiency of the external condenser type still were compared with conventional still under different conditions. A low power, variable speed fan was used to exhaust the water– vapor from the solar still to an external condenser as shown in Fig. 12. The following energy balance equations were used for basin, water mass and glass cover of the solar still components, respectively: mb C b ðdT b =dtÞ ¼ ð1  Rg Þð1  αg Þð1  αw ÞIðtÞs  qw  qb

ð148Þ

mw C w ðdT w =dtÞ ¼ ð1  Rg Þð1  αg Þαw IðtÞs þ qw  qr;w  g  qc;w  g  qeff ð149Þ mg C g ðdT g =dtÞ ¼ ð1  Rg Þαg IðtÞs þ qr;w  g þ qc;w  g  qc;g  a  qr;g  a þ ð1  ζ Þqeff

ð150Þ

The effect of vapor extraction from the solar still to the external condenser is represented by the term (1  ζ)qeff in the above expression. The factor ζ represents the fraction of water–vapor directed to the external condenser and is defined as

ζ ¼ ðMcondenser Þ=ðMevaporated Þ

ð151Þ

The effective water evaporation heat transfer rate (qeff) was found to vary linearly with the extraction ratio ζ as follows: qeff ¼ qe;w  g ð1 þ ϕζ Þ

ð152Þ

The value of constant Φ was found to be 0.8 by comparing the values for the numerical model with the experimental results. It was found that the increase in still efficiency achieved by the use of an external condenser was as high as 47%. Also the use of an external condenser reduced the negative effects of high wind speed on still efficiency. Haddad et al. [19] proposed a mathematical model for a basin type solar still integrated with a packed bed storage tank which was used as an external condenser. The condenser was cooled during the night using a radiative cooling panel by circulating pure water. As a result of this circulation, the cold fluid exiting the radiative panel charged the rock domain within the packed bed storage tank with coldness. This process continued during night until the tank attains the lowest possible temperature, which was very near to the effective sky temperature, provided that the radiative cooling panel area was large enough. At the beginning of the daylight, water was evacuated from the packed bed tank and it was used as a condenser to condense the vapor produced by the still. The schematic diagram of solar still coupled with packed bed condenser and radiative cooling panel is shown in Fig. 13. The effects of different design, climate and operating parameters on the modified still performance were investigated. Some of these parameters were found to be the ambient temperature, the effective sky temperature, the incident solar radiation and the

873

sizes of the solar still, the packed bed condenser and the radiative cooling panel relative to each other. The energy balance equation for basin, glass and packed bed storage tank are given as follows:Basin: IðtÞs ατ ¼ qr;b  g þ qe;b  pt þ qe;b  g þ qc;b  g þ qc;b  pt þ qr;b  pt þ ðmCÞb

∂T b ∂t

ð153Þ

Glass: qr;b  g þ qe;b  g þ qc;b  g ¼ qc;g  a þ qr;g  a Packed bed storage tank: h i dT pt M pt C pt ¼ Ab qe;b  pt þ qc;b  pt dt

ð154Þ

ð155Þ

The hourly yield per unit basin surface area of the still is given as mew ¼

qe;b  g þ qe;b  pt  3600 hfg

ð156Þ

where Apt qc;b  pt ¼ hc;b  pt ðT b T pt Þ Ab and qe;b  g ¼

ð157Þ

  ðP b  P g Þ M w hfg hc;b  g ðP T  P b ÞðP T  P g Þ M air C p;air

ð158Þ

  ðP b  P pt ÞP T Apt M w hfg hc;b  pt M air C p;air ðP T  P b ÞðP T  P pt Þ Ab

ð159Þ

qe;b  pt ¼

It was found that the effective sky temperature does not affect the still performance significantly. The still productivity increases by increasing the solar radiation, however the still efficiency decreases. Also, increasing the ambient temperature improves the still productivity due to reduction in thermal losses from the still to the surroundings. In the enhanced still, the condensation mainly occurs in the packed bed tank and it is not affected by increasing the ambient temperature. Fath and Hosny [20] presented a theoretical study of the thermal performance of a single sloped basin still with enhanced evaporation by adding black dyes and a built-in additional condenser. The proposed still was built so that one of its sides (condenser) is tilted to be parallel to sun rays and, therefore, always be in the shaded area as shown in Fig. 14. The built-in condenser acted as more effective heat and mass sink. The condenser could have internal and external fins to increase its effective surface area and improve its heat transfer effectiveness. Black dyes were placed inside the basin to increase basin’s absorptivity and evaporation surface area.

Fig. 12. Schematic of solar still with external condenser [18].

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The following energy balance equations were used for the thermal modeling: Basin water: Mw C w

dT w ¼ ðτg αw ÞIðtÞAb  Q e  Q c  Q r  Q b dt

ð160Þ

 mg C g

dT g dt



¼ ð1  Rg Þαg IðtÞs þ qr;w  g þ qc;w  g þ qe;w  g  hc;g  cf ðT g  T cf Þ

ð165Þ   dT cf _ cf ðC cf 1 T cf 1  C cf 2 T cf 2 Þ þ hc;g  cf ðT g  T cf Þ  qc;cf  a  qr;cf  a  qecf mcf C cf ¼m dt

ð166Þ

Glass cover: Mg C g

dT g ¼ αg IðtÞAb þ Q e;w  g þQ c;w  g þ Q r;w  g  Q c;g  a  Q r;g  sky dt ð161Þ

Condenser: M co C co

dT co ¼ Q e  co þ Q c  co þ Q r  co  Q c;co  a  Q r;co  sky dt

ð162Þ

where Q r ¼ Q r;w  g þQ r  co Q e ¼ Q e;w  g þ Q e  co Q c ¼ Q c;w  g þ Q c  co From the analysis, the parameters that most influence the productivity were found as condenser inner reflectivity, evaporation surface area, solar intensity, ambient temperature and base insulation effectiveness. The other parameters such as condenser material, mass, outer emissivity, surface area tilt angle, and wind speed were less influential on the still productivity. A combination of those influencing parameters was found to increase the still productivity by about 55% over conventional still. 7.1.10. Water film cooling over glass cover The effect of water film cooling of the glass cover on the efficiency of a single basin solar still was investigated numerically by Abu-Hijleh and Mousa [21]. The higher efficiency could be achieved by increasing the temperature difference between water in the basin and the glass cover. The investigation by the authors mainly focused on the flow of a water film over the glass cover in order to reduce the glass temperature. The schematic of the proposed system is shown in Fig. 15. The following energy balance equations were used for basin, water mass, glass cover and water in the cooling film, respectively. All the equations were written per unit area of the still and the areas of the glass cover and basin were assumed to be equal.   dT b mb C b ¼ ð1 Rg Þð1  αg Þð1  αw ÞIðtÞs qw  qb ð163Þ dt  mw C w

dT w dt



¼ ð1  Rg Þð1  αg Þαw IðtÞs þqw  qr;w  g  qc;w  g  qe;w  g  qmw

ð164Þ

where “qmw” is the heat energy required to heat the make-up water to the basin temperature. The following correlation has been used to determine the convection heat transfer coefficient (hc,g  cf) between the glass cover and cooling film: hc;g  cf ¼ 0:664ðK cf =LÞReL 1=2  Pr 1=3

where, “Kcf” is the thermal conductivity of water used for film cooling and “ReL” is the Reynolds number based on length L. It was observed that the flow of water film over the glass cover reduced the convection and radiation energy losses to the ambient as well as increased the condensation rate inside the glass cover. For enhancing the efficiency of the still, the best combination of film cooling parameters was found to be Lcf ¼ 5E  4 m and Vcf ¼ 1E  6 m3/s-m. It was found that the proper combination of cooling film parameters enhanced the still efficiency by about 20%. 7.1.11. Storage medium El-Sebaii et al. [22] presented transient mathematical model for a single basin solar still integrated with a thin layer of a sensible storage medium, beneath the basin liner of the still, for the purpose of fresh water production during night time. The thermal performance of the still with and without storage medium was investigated by computer simulation. The effects of mass flow rate and thickness of the flowing water for different masses of the storage material on the daylight, overnight and daily productivity and efficiency of the still were studied. Sand was used as a storage medium because it is cheap and easily available. Part of the thermal energy from solar radiation was transferred by convection to the water flowing over the basin liner and the other will be transferred by conduction to the sand beneath it. After sunset, the sand acts as the heat source for the basin water; consequently, the solar still continued to produce fresh water during the night. Fig. 16 shows the schematic diagram of the solar still integrated with the storage layer. The following energy balance equations have been used: Glass cover: IðtÞs αg þ ht;w  g ðT w  T g Þ ¼ hr;g  sky ðT g  T sky Þ þ hc;g  a ðT g  T a Þ

ð168Þ

Water mass: IðtÞs τg αw bdx þhb ðT b  T w Þbdx ¼ ht;w  g bdxðT w  T g Þ þ dw ρw C w _ wCw þm

Fig. 13. Schematic of the enhanced still with packed bed condenser [19].

ð167Þ

∂T w dx ∂x

∂T w bdx ∂t ð169Þ

Fig. 14. Basin still with an inherent built-in passive condenser and increased evaporation area [20].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

ðK b =Lb ÞðT b  T pcm Þ ¼ ðM equ =Ab ÞðdT pcm =dtÞ þ U b ðT pcm T a Þ

Basin liner: IðtÞs τg τw αb ¼ hb ðT b  T w Þ þ

Kb ðT  T sm Þ Lb b

ð170Þ

Kb M sm C sm dT sm þ U b ðT sm T a Þ ðT  T sm Þ ¼ Lb b Ab dt

Kb ðT  T pcm Þ Lb b

0

M pcm ðhfg Þpcm =Ab Δt ¼ hb ðT pcm  T b Þ þ U b ðT pcm T a Þ ð174Þ

ð171Þ

where Tsm, Msm and Csm are the temperature, mass and specific heat of the storage medium, respectively. It was found that the daily productivity decreases with increasing the mass of sand. After sunset, sand acts as the heat source for the basin water until the early morning of the next day. The daily productivity and efficiency were found to increase with increasing the thickness of the basin liner until an optimum value of 0.003 m, beyond which those values decreased slightly with further increase in the thickness. Also the daily productivity and efficiency decrease with an increase of thermal conductivity of the basin liner material. The annual average of daily productivity with 10 kg of sand is found to be higher than that without sand by 23.8%. El-Sebaii et al. [23] presented a transient mathematical models for a single slope single basin solar still with and without phase change material (PCM) under the basin liner of the solar still. A thin layer of stearic acid as a PCM was integrated beneath the basin liner to enhance the overnight productivity of the still. The performance of the modified still was investigated by computer simulation. The energy balance equations for various elements of the still as well as for the PCM during charging and discharging modes were formulated and solved analytically. The schematic diagram of the investigated solar still with built-in PCM as a storage medium is shown in Fig. 17. Part of thermal energy from the sun is transferred by convection to the basin water and the other will be transferred by conduction to the PCM beneath the basin liner. When the basin liner temperature becomes higher than that of the PCM, heat is first stored as a sensible heat till the PCM reaches its melting point. Then, the PCM starts to melt and the heat will be stored in the melted PCM as a sensible heat. When the solar radiation decreases, the still components starts to cool down, the liquid PCM transfers heat to the basin liner and from the latter to the basin water until the PCM completely solidified. In other words, the PCM will act as a heat source for the basin water during low intensity solar radiation periods as well as during the night; consequently, the still continues to produce fresh water after sunset even with thin layers of basin water. The energy balance equations for basin liner and phase change material (charging mode) are given by ð172Þ

Fig. 15. Schematic of water film cooling over the glass cover of solar still [21].

ð173Þ

For a selected time interval Δt, the energy balance equation for phase change material (discharging mode) is given by For T pcm ¼ T ml

Storage medium:

IðtÞs τg τw αb ¼ hb ðT b  T w Þ þ

875

For T pcm a T ml

0

hb ðT pcm  T b Þ þ U b ðT pcm T a Þ ¼ ðM equ =Ab ÞðdT pcm =dtÞ ð175Þ

where h0 b ¼ Kpcm/Lpcm is the conductive heat transfer coefficient from the PCM to the basin liner. The still performance with and without PCM was studied by computer simulation on typical summer and winter days. It was found that the daily productivity is found to decrease slightly with increasing the mass of PCM. But the overnight and daily productivities are significantly increasing with the increase in the mass of PCM. Comparisons between the results obtained for the still with and without the PCM showed that, using 3.3 cm of stearic acid under the basin liner, 9.005 (kg/m2/day) of fresh water can be obtained on a summer day with a daily efficiency of 84.3% compared to 4.998 (kg/m2/day) when the still is used without PCM. The PCM becomes more effective at lower masses of basin water during the winter.

7.1.12. Vapor adsorption Kannan et al. [24] designed a vapor adsorption type solar still utilizing an absorbent bed pipe network comprising activated carbon–methanol pair embedded in the basin, as shown in Fig. 18. In this modified still, an inner pipe of 0.025 m diameter is enclosed with an outer pipe (diameter of 0.05 m) sealed at both ends. The space between the inner and the outer pipes contains an activated carbon–methanol pair acting as an adsorbent bed. During the day time, brackish or saline water is circulated from a storage tank through the inner tube where water is preheated and collected in collection tank. It is pumped back to the storage tank for continuous circulation. Therefore preheated water is supplied as a feed to the basin during the day time. During the night time heat will be released to saline water in the basin through the liberation of latent heat from the methanol vapor and the sensible heat from the activated carbon. Hence both day and night time the evaporation will be enhanced. The temperature of the saline water was further augmented by means of adding the sensible heat storage materials like sponge, gravel, sand and black rubbers on the basin to increase the exposure area to solar radiation . The energy balance equation of vapor adsorption type solar still including the sensible heat gain by the activated carbon and latent

Fig. 16. Schematic of single basin solar still with sensible storage medium [22].

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Basin liner:

heat gain by the methanol is given as   dT b þ M met ðhfg Þmet þ Q w þ Q loss IðtÞs Ab αb ¼ ðM b C b þ M act C act Þ dt

Q sun;b ¼ Q sun;dr þ Q sun;df þ Q sun; int þ Q sun;ext ð176Þ

The energy balance equation of vapor adsorption type solar still with sponge and gravel is given by  
 dT b IðtÞs Ab αb ¼ M b C b þ M act C act þ Mgr C gr þ M met ðhfg Þmet þ Q w þ Q loss dt

IðtÞs Ab αb ¼ ðMb C b þ Mact C act þ Msa C sa Þ

  dT b þ M met ðhfg Þmet þ Q w þ Q loss dt

ð178Þ

The energy balance equation of vapor adsorption type solar still with sponge, sand and black rubber is given by 

 dT b IðtÞs Ab αb ¼ ðMb C b þ Mact C act þ Msa C sa þ M br C br Þ þ M met ðhfg Þmet þ Q w þ Q loss dt

ð179Þ The energy balance equation of saline water is given by   dT w ð180Þ IðtÞs Aw αw þ Q w ¼ Q c;w  g þ Q r;w  g þ Q e;w  g þ M w C w dt The energy balance equation of glass cover is given by IðtÞs Ag αg þ Q c;w  g þ Q r;w  g þ Q e;w  g ¼ Q r;g  sky þ Q c;g  sky þ Mg C g



dT g dt



Glass cover: Q sun;g ¼ IðtÞg αg   αg  cos ðφ  γ Þ þ blb 1 þ tan θ Q =τ ðβ Þ þ Q sun;df =ðτg Þdf αb sun;ext g g tan ϕ

ð183Þ

ð177Þ

The energy balance equation of vapor adsorption type solar still with sponge and sand is given by

ð182Þ

where Qsun,b and Qsun,g are the solar radiation absorbed on the basin liner and glass cover. The energy balance equations for the still with internal reflector only: Basin liner: Q sun;b ¼ Q sun;dr þ Q sun;df þ Q sun; int

ð184Þ

Glass cover: Q sun;g ¼ IðtÞg αg    αg
cos ðφ  γ Þ þ blb 1 þ tan θ Q =ðτ Þ αb sun;df g df tan ϕ

ð185Þ

The energy balance equations for the still without reflector: Basin liner: Q sun;b ¼ Q sun;dr þ Q sun;df

ð186Þ

Glass cover: ð181Þ

The performance of the modified solar still was compared with that of the conventional still and it was found that the distillate production rate in the vapor adsorption was ranged between 3.1 and 4.3 kg/m2 while in the conventional still the distillate production rate was between 1.9 and 2.3 kg/m2. The night time distillate production rate of the novel still was two times than the conventional solar still. Also the maximum distillate production rate and daily efficiency was obtained in the vapor adsorption solar still with sand, sponge and black rubber combinations. It was concluded that the maximum deviation between theoretical and experimental analyses was less than 6%. 7.1.13. External reflector Tanaka and Nakatake [25] presented a theoretical analysis of a basin type solar still with internal and external reflectors. The effect of both internal and external reflectors on the amount of solar radiation absorbed on a basin liner as well as distillate productivity of the single slope solar still was found theoretically at 301N latitude. Fig. 19 shows the proposed still which consists of a basin liner, glass cover, two sides and back walls, and a vertical external reflector extending from the back wall of the still. The two sides and back walls are assumed to be covered with highly reflective materials, so these walls serve as the internal reflectors. The energy balance equations for the still with internal and external reflectors are expressed as follows:

Q sun;g ¼ IðtÞg αg    αg
cos ðφ  γ Þ blb 1 þ tan θ Q =ðτ Þ þ αb sun;df g df tan ϕ

ð187Þ

Based on the theoretical analysis, it was found that the increase in daily yield amounts of distillate for the entire year by adding both internal and external reflectors is averaged as 48%, and that by adding the internal reflector only is averaged as 22%, when the angle of the glass cover is 201. Also, the benefit of internal and external reflectors is negligible in the summer time due to shadow effect and for a still of glass cover angle at 401; the benefit of external reflector is negligible during winter season. Tanaka and Nakatake [26] presented another theoretical analysis of a basin type solar still with an internal reflector and an inclined flat plate external reflector during winter season at 301N latitude. The solar still consists of a basin liner, a glass cover, two side walls, a back wall, and an inclined flat plate external reflector of highly reflective materials (Fig. 20). The two sides and back walls of the still are assumed to be covered with highly reflective materials, so these walls serve as the internal reflector. The shadows of internal and inclined external reflector are shown in Fig. 21. Direct solar radiation absorbed by the basin liner may be expressed as Q sun;dr ¼ IðtÞdr τg ðβ g Þαb  blb

ð188Þ

Solar radiation reflected by the internal back wall reflector and absorbed on the basin liner is expressed as Q sun; int ¼ IðtÞdr τg ðβ g ÞRint αb  blb tan θ

cos φ tan φ

ð189Þ

Solar radiation reflected by the external reflector and absorbed on the basin liner is expressed as

 l4 1 ð190Þ Q sun;ext ¼ IðtÞdr τg ðβg ÞRext αb  l1 b  ðl2 þ l3 Þ 2 l1 The values of l1, l2, l3 and l4 are determined from the shadow diagram. Diffuse solar radiation absorbed by the basin liner may be expressed as Fig. 17. Schematic diagram of single slope single basin solar still with PCM [23].

Q sun;df ¼ IðtÞdf ðτg Þdf αb  blb

ð191Þ

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

877

Fig. 18. Schematic diagram of vapor adsorption type solar still [24].

Angle of glass cover is expressed as ðτg Þdf ¼  2:03  10  5  θ  2:05  10  3  θ þ 0:667 2

ð192Þ

It was found from the theoretical calculations that the inclined external reflector increased the daily productivity of the still at any glass cover angle, and the external reflector angle should be set at about 151 from vertical on a winter solstice day. When the angle of the glass cover is 401, the benefit of the vertical external reflector is negligible, while the inclined external reflector can effectively reflect the sunrays to the basin liner. Also the daily amount of distillate yield of the still with the inclined external reflector would be about 16% greater than that with the vertical external reflector. 7.1.14. Packed layer Abdel-Rehim and Ashraf Lasheen [27] presented the governing equations for a modified solar desalination system, using a packed layer that was installed in the bottom of the basin to increase the efficiency of the still. The packed layer was formed from glass balls of 13.5 mm diameter as simple thermal storage system. Another modification was done in the solar still, using rotating shaft installed close to the basin water surface. The rotating shaft was used to break boundary layer of the basin water surface, thus increasing the water vaporization and condensation. The rotating shaft was powered by a small photovoltaic system as shown in Fig. 22. The packed layer was used to assist the desalination process during the sunrise and after the sunset. The thermal equations of the packed layer are given as qpkd1 ¼ mpkd C pkd

∂T pkd1 ¼ Apkd IðtÞs ðατÞpkd þ Aw IðtÞs ðατÞw  qLpkd During sunset ∂t

ð193Þ qpkd2 ¼ mpkd C pkd

∂T pkd2 ∂T pkd1 ∂T w ¼ mpkd C pkd þ mw C w  qLpkd After sunset ∂t ∂t ∂t

ð194Þ where qLpkd is the heat losses between packed layer and saline water. Based upon the results obtained, it was found that the modifications done on the conventional solar still enhanced the performance significantly. The fresh water productivity for the modified still used packed layer was found higher than the productivity of modified still

Fig. 19. Heat transfer in a solar still with internal and external reflectors [25].

used rotating shaft. The efficiency of modified solar desalination system used packed layer thermal energy storage was increased by 5–7.5%, while for the modified still used rotating shaft and photovoltaic system it was increased by 2.5–5.5% than the conventional still.

7.1.15. Key findings and discussion on thermal models of passive solar still The various design modifications of passive solar stills and the corresponding changes in their energy balances were elaborated in the above section. From the detailed review, it is observed that most of the researchers used the well-known Dunkle’s model to predict the performance of the modified solar stills and altered the basic energy balance equations by introducing or neglecting few parameters. The thermal modeling of any solar desalination system is developed based on the energy balances for its components. These energy balances mainly depend on the design and climatic

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parameters of the distillation unit. From the review, it is observed that the accurate estimation of temperature dependent internal heat transfer coefficients is the most important task for the prediction accuracy of any thermal model. Many researchers tried to describe the empirical correlations for evaporative, convective and radiative heat transfer coefficients for t heir theoretical predictions. Also the relationships between the heat and mass transfer coefficients and various operational, climatic and design parameters of the still were reported in the literature. Based on the observations, the evaporative fraction of internal heat transfer within the still is found highest irrespective of the seasons. However, the internal convective heat transfer coefficient decreases with the increase of water depth in the basin due to decrease in water temperature. The trend of water productivity is always similar to the trend of convective heat transfer coefficient. The convective and evaporative heat transfer coefficients have more influence on the still productivity than the radiative heat

Fig. 20. Schematic of a solar still with internal reflector and an inclined external reflector [26].

Fig. 21. Shadow of internal reflector and shadow and reflected projection of inclined external reflector [26].

transfer coefficient. Also, the internal heat transfer coefficients evaluated by using inner surface glass temperature are found best suitable for the thermal modeling of a solar still rather than using glass temperature for the same. While using jute cloth as an absorbing medium between the water surface and glass cover, the radiation heat transfer coefficient term is neglected during the evaluation of distillate output rate. In case of floating porous absorbers, it is inferred that the heat transfer coefficient of the floating insulation has a significant effect on the distillate output. However, when using these kinds of absorbers, quicker start-up times as well as higher operating temperatures were achieved resulting in higher distillate yield. But the life times of these absorbing materials are quite shorter and need frequent replacement thus limit their real time implementation. Generally, the side heat loss term for passive solar still is neglected to make the analysis simple. But, in deep basin solar stills, it is inferred that the side heat loss is significant due to higher water depth and it must be included during their thermal analysis to make the performance prediction more accurate. The application of double glass cover, double condensing chamber, water film cooling over glass cover and external reflector with the passive solar still were also reported. The double glass cover solar still system minimized the formation of water droplets on the inner surface of the inner glass, which are responsible for reflecting/absorbing some of the incident radiation. In double condensing chamber solar still, the diffusion of vapors was considered in its energy balance by using diffusion coefficient. In these types of designs, diffusion coefficient is included in thermal analysis due to transfer of water vapor from one chamber to another chamber. These complex design modifications certainly decrease the heat losses by convection to the ambient resulting in high basin water temperature but provide a lot of operational constraints and need at most care and maintenance. In the same way, applying vacuum inside the solar still increases the productivity remarkably due to absence of the convection heat loss. But this will incur some additional investment and operational costs for its implementation. The increase of the evaporation surface area of the still by using sponge, wick, fins, floating perforated black plate, suspended absorber, etc was also reported in the literature. It is inferred that increasing the evaporation surface within the basin water of a conventional still decreases the preheating time required for evaporating the still water. The respective increase in area and thermal conductivity of materials were included while formulating energy balance equations. It is found from the analysis that this kind of design modifications did not increase the still’s productivity considerably and could not be implemented for higher distilled output requirements. Few researchers used the specific heat of saline water, calculated in terms of saline water temperature and salinity of water, instead of using a constant value for all kinds of analyses. The utilization of storage medium like sand, phase change material, etc. was also experimentally investigated by some researchers. The effect of these materials in terms of thermal capacity, mechanical properties of materials and area were included in the thermal analysis. But, the improvement in productivity is not up to the level of expectation. From the above analysis, it is concluded that the Dunkle’s model may be used to predict the performance of the passive solar stills by incorporating appropriate deign and operational parameters in their energy balances. However, this model may not provide an accurate solution due to its limitations (assumptions). The flow characteristics of the fluid and physical properties of the fluid at different operating temperature range are not considered while the formulation of basic evaporative and convective heat

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

879

Fig. 22. Schematics of modified solar still with packed layer and rotating shaft [27].

transfers phenomena. Also, Dunkle’s model is not valid for double slope passive still due to temperature and solar radiation of both the condensing surfaces are different at any point of time. The constants C and n are most influencing variables in calculating various heat transfer coefficients and it is taken as a common value for all different operating temperatures in Dunkle’s model. In practical cases, it may vary based on the temperature and geometry of solar still. 7.2. Single basin single slope active solar still The thermal models have also been developed by many researchers for active solar stills by augmenting various renewable energy devices. The following section categorizes the work carried out on the performance prediction of the active solar stills based on the type of energy device coupled with them. 7.2.1. Flat plate collector Rai and Tiwari [28] theoretically investigated the transient performance of a single basin solar still coupled with a flat plate collector with variation in insulation thickness, absorbance of water and neglecting the heat capacity of the glass cover. The effect of adding dye with the basin water was also investigated. The water is circulated between the still and the flat plate collector with the help of a small pump as shown in Fig. 23. The following energy balance equations were used for glass cover, water and basin liner, respectively: ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g T a Þ ðmCÞw

dT w ¼ α0w IðtÞs þ hw ðT b  T w Þ  ht;w  g ðT w T g Þ þ Q u dt

α0b IðtÞs ¼ hw ðT b  T w Þ þ hb ðT b  T a Þ

ð195Þ ð196Þ ð197Þ

The useful energy derived from active solar still is given as:

ð198Þ Q u ¼ AC F R ðατÞC IðtÞC  U LC ðT w  T a Þ The heat removal factor of the flat plate collector (FR) is given by    _ w AC U LC F 0 mC ð199Þ FR ¼ 1  exp  _ w AC U LC mC It was found that the effect of insulation thickness and absorbance of water is almost similar in nature to that of an uncoupled single basin solar still, but the water distillate from the coupled solar still is

Fig. 23. Schematic of single basin solar still coupled with flat plate collector [28].

24% higher than that of the uncoupled solar still. Also it was inferred that the daily distillate output per unit area in both stills increases with increasing insulation thickness up to 4 cm rapidly and asymptotically afterwards. The use of dye in the water increases the daily distillate output, but the rate of increase with the absorptance is more in uncoupled still than the coupled still. Sodha et al. [29] developed a techno-economic model for a solar still coupled with a flat plate collector through a heat exchanger based on the establishment of periodic steady state conditions (Fig. 24). The heated water from the solar collector is circulated through a coil-type heat exchanger which is immersed in the basin water. During no or low sunshine hours, the solar collector is decoupled from the solar still. The following energy balance equations were used for thermal analysis: Glass cover:

α0g IðtÞh Ag þ ht;w  g ðT w  T g ÞAw ¼ ht;g  a ðT g T a ÞAg

ð200Þ

Basin water:

α0w IðtÞh Aw þ FðtÞQ u ¼ M w C w

dT w þ ht;w  g ðT w T g ÞAw dt

þ ðU b Aw þU ss Ass ÞðT w  T a Þ þU pc Apc ðT w  T a ÞFðtÞ ð201Þ

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where

where h α α0w ¼ αw þ w b hw þ hb

ð202Þ

And F(t) is a step function of time controlling the operation of the solar collectors. Its values are given below: F ðt Þ ¼ 1; during sunshine hours when the solar collector is coupled with the solar still ¼ 0; during no or low sunshine hours when the solar collector is decoupled Solar collector:   T C;out T a  ððατÞIðtÞC =U LC Þ F 0 U LC AC ¼ exp  _ C Cw T C;in T a  ððατÞIðtÞC =U LC Þ m

ð203Þ

Heat exchanger: _ hxf C w m

dT hxf ðxÞ Δx ¼  π DU hx ðT hxf  T w ÞΔx dx

ð204Þ

The internal heat and mass transfer coefficients of the solar still were evaluated based on Dunkle’s model. Numerical calculations were made for different combinations of collector area, still area and heat exchanger lengths. It was concluded that the addition of the solar collector enhances the distillate yield; however it was not always economical. Lawrence and Tiwari [30] developed a theoretical thermal model of the solar still coupled with a panel of collectors through a parallel tube heat exchanger working under natural circulation mode by incorporating the effect of various still and system parameters. The collector closed loop, consisting of heat exchanger and collector, is filled with anti-freeze working fluid and water is filled in the basin at least up to a depth so the heat exchanger is dipped in the water. The working fluid gets heated by solar radiation in the collector and starts rising in the upward direction. Then the heat is transferred from the working fluid to the water in the basin by conduction and the working fluid becomes cooler and goes into the collector after releasing its heat into the basin. The energy balances of the system are as follows:Glass cover: ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g T a Þ

ð205Þ

Basin liner: ðατÞb IðtÞs ¼ hw ðT b T w Þ þ hb ðT b T a Þ

ð206Þ

Water mass: ðατÞw IðtÞs þhw ðT b  T w Þ þQ u ¼ mw C w

dT w Ass þ ht;w  g ðT w  T g Þ þ hb ðT w T a Þ dt Ab


 P w0  P g0  he;w  g ¼ 0:03 
T w0  T g0

ð212Þ

Also it was found that the efficiency of the high temperature distillation system is lesser than the normal operating temperature system. And the efficiency decreases with increase of water depth in normal operation, while the results are reversed in high temperature distillation. Tiwari and Dhiman [31] studied the performance of a solar still integrated with a panel of collectors through a heat exchanger and presented the thermal analysis by incorporating the effect of all possible system parameters. The system used in this analysis is shown in Fig. 25. The effect of temperature dependence of internal heat transfer coefficients on the performance of the solar still was analyzed and the theoretical results have been validated through experimental data. The following energy balance equations were used at various components of the system: Glass cover: ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g  T a Þ

ð213Þ

Water mass: Ab M w

dT w ¼ Ab α0w IðtÞs þ ðAb  Ahx Þhw ðT b T w Þ  ht;w  g Ab ðT w  T g Þ þ Q u dt

ð214Þ Basin liner:



ðAb Ahx Þα0b IðtÞs ¼ ðAb  Ahx Þ hw ðT b  T w Þ þ hb ðT b  T a Þ Heat exchanger:



_ hxf π ðD=2Þ U dx U α0hx IðtÞs ¼ mC

 dT hxf þ ht;hxf  w ðT hxf  T w Þ dx dx

Collector panel:   ðατÞIðtÞC T C;out ¼ T a þ ð1 þ HÞ þ T C;in H U LC

ð215Þ

ð216Þ

ð217Þ

where _ hxf Þ H ¼ expð F 0 U LC AC =mC

ð218Þ

Q u ¼ hhxf Lhx ðT hxf  T w Þ

ð219Þ

H 2 1 T hxf ¼ T R þ ðT C;out  T R Þ H 1 Lhx

ð220Þ

H 2 ¼ expðH 1 Lhx Þ

ð221Þ

ð207Þ The useful energy supplied from the panel of collectors to basin water through the heat exchanger is given as

ð208Þ Q u ¼ F 0 C 1 ðατÞC IðtÞC AC  C 2 ðUAÞC ðT w TÞa =Ab where C1 ¼ C2 þ

C2 ¼

ðUAÞpc ðUAÞhx þ ðUAÞpc þ F 0 ðUAÞC

ðUAÞhx ðUAÞhx þ ðUAÞpc þ F 0 ðUAÞC

ð209Þ

ð210Þ

Based on the numerical results, the following empirical relation was derived for total heat transfer coefficient from water surface to glass cover for an operating temperature range of 30–90 1C: ht;w  g ¼ 8:71 þ he;w  g

ð211Þ

Fig. 24. Schematic diagram of solar still coupled with a flat plate collector and a heat exchanger [29].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

_ hxf H 1 ¼  hhxf =mC

ð222Þ

and TR ¼ Tw þ

π ðD=2Þα0hx IðtÞC

ð223Þ

hhxf

From the numerical calculations, it was found that varying the flow rate of the liquid through the heat exchanger and the length of the heat exchanger does not affect the performance of the system significantly. Also the overall efficiency of the system varies between 15% to 19%. It was argued that the bottom insulation is an important design parameter of the solar still, even though it is coupled with collectors. Kumar et al. [32] derived analytical expressions for water and glass cover temperatures and yield in terms of design and climatic parameters. An attempt was made to optimize the inclinations of the collectors and solar still glass covers for maximum daily or annual yield. The schematic diagram of the solar still coupled with flat plate collector is shown in Fig. 26. The energy balances for different components of the system are described as follows: Glass cover:

αg IðtÞs Ag þ ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g T a ÞAg Basin liner:



ð224Þ

αb ð1  αg Þð1  αw ÞAb IðtÞs ¼ hw ðT b  T w Þ þ hb ðT b  T a Þ Ab

dT w þ ht;w  g ðT w  T g ÞAw dt

ð226Þ where



Q u ¼ AC F R ðατÞC IðtÞC  U LC ðT w  T a Þ

ð227Þ

The following relations were derived, by solving the energy balance equations, for water and glass cover temperatures:     f ðtÞ 1  expð aΔtÞ 1  expð  aΔtÞ 1 þ T w0 ð228Þ Tw ¼ a a Δt aΔt Tg ¼

αg IðtÞg þ ht;w  g ð cos θÞT w þ ht;g  a T a ht;w  g ð cos θÞ þht;g  a

and the effect of different condensing cover materials. Plastic, copper and glass were used as condensing cover materials in the solar stills. Also the effects on various parameters on yield such as thickness of glass cover, collector absorbing surface, wind velocity, water depth, etc. were predicted theoretically and the results were validated through experimental data. A panel of flat plate collectors was coupled in case of active solar still to feed additional thermal energy to the basin water. The energy balances equations of the system are as follows: Inner and outer glass cover:

α0g Ieff þ ht;w  g ðT w  T gi Þ ¼

Kg ðT T go Þ Lg gi

Kg ðT  T go Þ ¼ ht;g  a ðT go  T a Þ Lg gi

ð230Þ ð231Þ

Basin liner:

α

0 b I eff

¼ hw ðT b T w Þ þ hb ðT b  T a Þ

ð232Þ

Water mass: Q u þ α0w ð1  α0g ÞI eff þ hw ðT b  T w Þ ¼ ðmCÞw

dT w þ ht;w  g ðT w  T go Þ dt ð233Þ

where ð225Þ

Water mass: Q u þ αw ð1  αg ÞAw IðtÞs þ hw ðT b  T w ÞAb ¼ Mw C w

881



Q u ¼ AC F R ðατÞC IðtÞC  U LC ðT w T a Þ

ð234Þ

The coefficient of correlation (r) between predicted and experimental values showed fair agreement with 0.90oro0.99 and root mean square percent deviation between 3.22% and 22.64%. It was observed that the inner glass temperature plays a key role to determine the yield. It was also found that the yield increases with increase of collector surface area. The effect of wind velocity on the yield is also significant. As the wind velocity increases, the convective heat transfer coefficients from the glass cover to ambient air increases which in turn increase the overall yield. But the yield rate decreases with increase of water mass in the basin. It was also observed that the yield is directly related to thermal conductivity of condensing cover materials; copper gives a greater yield compared to glass and plastic due to higher thermal conductivity.

ð229Þ

On the basis of the numerical computations, it was found that the optimum inclination of collector is 201 and for the still glass cover is 151. Also the annual yield decreases with an increase of water depth in the solar still basin. Singh and Tiwari [33] evaluated the monthly and annual performance of both active and passive solar stills by numerical computations for different Indian climatic conditions. The analysis was based on quasi-steady-state condition. In active solar still, flat plate collector was utilized to provide additional thermal energy (Qu) to the basin water. The energy balance equations for glass cover, basin liner and water mass of the active solar still are same as the equations described by Kumar et al. [32]. Numerical computations were performed to determine monthly and annual yields of both passive and active solar stills by considering the climatic parameters at five stations. The analytical expressions were also derived for water temperature, glass cover temperature and yield as a function of climatic parameters and design parameters. It was inferred from the analysis that the annual yield significantly depends on water depth and the annual yield for a given water depth increases linearly with collector area. It was concluded that the annual yield is at its maximum when the condensing glass cover inclination is equal to the latitude of the place. Dimri et al. [34] investigated the effects of inner and outer glass temperatures on the yield of both passive and active solar stills

7.2.2. Evacuated tube collector In evacuated tube collector, the sun rays are perpendicular to the surface of the glass throughout the day due to its cylindrical shape. The efficiency of this type of collector is always higher than the flat plate collector since the evacuated tubes greatly reduce heat losses as vacuum is present in the tubes. Sampathkumar et al. [35] developed a thermal model for the single basin solar still coupled with evacuated tube collector using energy balance equations. Fig. 27 shows the schematic diagram of

Fig. 25. Schematic of solar still coupled with panel of collectors and heat exchanger [31].

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the solar still coupled with evacuated tube collector. Experiments were conducted to predict the performance of the proposed system. Also the effects of water depth and various heat transfer coefficients were analyzed. The theoretical model was validated by the experimental results and the closeness between the theoretical and experimental values was found in terms of coefficient of correlation and root mean square percentage deviation. The energy balances equations for various components of the system are described as follows: Glass cover:

α0g Ieff þ qr;w  g þ qc;w  g þqe;w  g ¼ qr;g  a þqc;g  a

ð235Þ

Inner surface of glass cover:

α0g IðtÞs þ ht;w  g Ab ðT w  T gi Þ ¼ hcd;gi  go Ag ðT gi  T go Þ Outer surface of glass cover: hcd;gi  go Ag ðT gi  T go Þ ¼ ht;g  a Ag ðT go  T a Þ

i dT w h þ qr;w  g þ qc;w  g þ qe;w  g dt ð236Þ

Basin liner:

α0b ð1  α0g Þð1  α0w ÞIeff ¼ qw þ qb

ð237Þ

The convective heat transfer coefficient between water and glass cover is given by hc;w  g ¼

Kf CðGrPrÞn df

ð238Þ

The values of “C” and “n” in the above expression were calculated using experimental results by regression analysis method. The useful energy supplied to the still through evacuated tubes is given as     AL Q u ¼ AET F R ðατÞET IðtÞET  U LET ð239Þ ðT w  T a Þ AET where, AET is equal to diameter of the outer glass tube  total length of the tubes in the evacuated tube collector and AL ¼ πAET. It was found that the daily productivity of the evacuated tube solar still was 72% higher than the passive solar still. It was inferred that the convective and evaporative heat transfer coefficients had more influence on the still productivity than the radiative heat transfer coefficient. Also the developed thermal model gave very good agreement with experimental results. Singh et al [36] presented a thermal model to predict the performance of evacuated tube collector (ETC) integrated solar still in natural circulation mode (Fig. 28). The performance of the system was predicted theoretically in terms of water and glass temperatures, yield, energy and exergy efficiencies. The system was optimized for the number of evacuated tubes integrated and water depth in basin for nearly the same maximum water temperature attainable by a single larger ETC. The following energy balance equations were used for various components of the solar still:

ð241Þ

Basin liner:

α0b IðtÞs Ab ¼ hw Ab ðT b  T w Þ þ hb Ab ðT b  T a Þ

ð242Þ

Water mass in the evacuated tubes: At N tc IðtÞC η0  a0 At N tc ðT wc  T a Þ ¼ M wc C w

Water mass: Q u þ α0w ð1  α0g ÞI eff þ qw ¼ mw C w

ð240Þ

dT wc _ w ðT wc  T w Þ þ N tc mC dt ð243Þ

where a0 is the solar collector efficiency coefficient. Water mass of the solar still: _ w ðT wc  T w Þþ α0w Ab IðtÞs þ hw Ab ðT b  T w Þ ¼ ht;w  g Ab ðT w  T gi Þ þ M w C w N tc mC

dT w dt

ð244Þ On the basis of the study, it was found that the maximum daily energy and exergy efficiencies were about 33.0 % and 2.5%, respectively, and the maximum daily yield was found to be 3.8 kg/m2 for 0.03 m basin water depth. Also the evaporative fractional exergy dominates over the radiative and convective fractions at most of the time. To make the system efficient, it was suggested that smaller size of ETC with ten number of tubes is preferable than a single unit the larger size ETC integrated. 7.2.3. Concentrator collector Singh et al. [37] developed analytical expressions for the water temperature of an active solar distillation unit with flat plate and concentrator collectors in terms of system and climatic parameters. The schematic diagrams of the solar still with a flat plate collector and with a concentrator are shown in Figs. 29 and 30, respectively. The solar still was placed at a higher position than the collector or concentrator to create sufficient pressure for thermosyphon flow. The energy balances for the different components are as follows: Glass cover: ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g  T a Þ

ð245Þ

Basin liner: ðατÞb IðtÞs ¼ hw ðT b  T w Þ þhb ðT b  T a Þ

ð246Þ

Water mass: ðατÞw IðtÞs þ hw ðT b  T w Þ þ Q u =Ab ¼ mw C w

dT w Ass þ ht;w  g ðT w  T g Þ þ hb ðT w  T a Þ dt Ab

ð247Þ The rate of thermal energy fed into the basin water is expressed as follows:

Q u ¼ F 0 AC ðατÞC IðtÞC  U LC AC ðT w  T a Þ For flat plate collector ð248Þ 0

Q u ¼ F Aa ðατÞC IðtÞC  U LC Ar ðT w  T a Þ For concentrator collector ð249Þ

Fig. 26. Schematic of solar still coupled with flat plate collector [32].

From the analysis, it was observed that the thermal losses from the receiver of the concentrator collector are significantly reduced due to its small surface area in comparison to that of the flat plate collector. It was found that the efficiency of the solar still coupled with the concentrator is higher than that with the flat plate collector. Also the evaporative heat transfer coefficient in the case of concentrator will be higher than the flat plate collector. Abdel-Rehim and Ashraf Lasheen [38] conducted experimental and theoretical analysis of a solar desalination system coupled with a solar parabolic trough with focal pipe and a simple heat exchanger. To transfer heat from parabolic concentrator to the

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883

Fig. 27. Schematic of single basin solar still coupled with evacuated tube collector [35].

solar still basin water through heat exchanger, oil was selected as a working fluid. The oil was forced flow using small pump which might be powered by PV system. Fig. 31 shows the schematic of the modified solar still coupled with parabolic trough concentrator and simple heat exchanger. The energy balance equations of the proposed system are expressed as follows: Glass cover: qg;in ¼ ðατÞw IðtÞs qc;g  a  qr;g  a

ð250Þ

where qg,in is the input thermal energy to the glass cover. Water mass qw;in ¼ ðατÞw IðtÞs  qe;w  g  qr;w  g  qc;w  g qoil  qLb

ð251Þ

In the above expression, qw,in is the input thermal energy to the basin water and qLb is the heat loss from the basin base to the ground. The rate of heat transfer from oil to basin water (qoil) due to heat exchange is given by the following relations:

_ p ðT in  T out Þ oil ð252Þ qoil ¼ mC The overall heat transfer coefficient of heat exchanger is determined by: U hx ¼

qoil AΔT oil

ð253Þ

The heat loss from the basin base to the ground is expressed as qLb ¼ ht;b  a ðT b T a Þ

ð254Þ

It was found that the fresh water productivity increased by an average of 18% due to the modification in the design. 7.2.4. Solar pond Velmurugan and Srithar [39] presented experimental and theoretical analysis of a mini solar pond assisted solar still for different salinity values. The productivity of pure water with and without sponge cubes in the still was also investigated. The water is preheated by using a mini solar pond, before sending it to the solar still through a copper heat exchanger as shown in Fig. 32. Theoretical analysis was conducted to find out the temperature of solution in solar pond and solar still by assuming both the initial temperatures were equal as ambient. The temperature of the thermal energy storage zone, known as Lower Convective Zone (LCZ), at the end of time interval “dt” is given by, h i n o Asur hðzÞIðtÞg þ K w T a =dncz þ T t =dt 


T t þ dt ¼
ð255Þ M pow C sw =dt þ Asur K w =dncz The specific heat of saline water (Csw) in terms of saline water temperature and its salinity is calculated by the following relation: C sw ¼ a1 þ a2 T w þ a3 T 2w þ a4 T 3w

ð256Þ

Fig. 28. Schematic of ETC integrated solar still [36].

where a1 ¼ 4206:8  6:6197s þ 1:2288  10  2 s2

ð257Þ

a2 ¼  1:1262 þ 5:4178  10  2 s 2:2719  10  4 s2

ð258Þ

a3 ¼ 1:2026  10  2  5:5366  10  4 s þ 1:8906  10  6 s2

ð259Þ

a4 ¼ 6:8774  10  7 þ 1:517  10  6 s  4:4268  10  9 s2

ð260Þ

where “s” is the salinity of the input water to the solar pond. It was observed that the average increase in productivity of the solar pond integrated still is about 27.6% and the maximum deviation in the yield is about 9% in comparison with that of the theoretical analysis. Also it was found that the optimum value of salt concentration in the mini solar pond is 80 g/kg for maximizing the temperature of Lower Convective Zone (LCZ). The average distillate productivity of the mini solar pond integrated with sponged still is 57.8% more than the productivity of ordinary still. The results obtained from the theoretical analysis gave very good agreement with the experiments and the maximum deviation was less than 10%. El-Sebaii et al. [40] studied the performance of a single basin single slope solar still integrated with a shallow solar pond with a heat exchanger welded to the pond absorber plate under the open cycle mode of operation to improve its daily productivity. The cold water from an insulated tank was used as a fluid flowing through the heat exchanger to extract the heat from the solar pond under open cycle continuous flow heating mode. The heat exchanger outlet was connected to the still via an insulated pipe to minimize heat losses. The heated fluid obtained at the outlet of the pond’s heat exchanger was fed at the inlet of the still to flow as a thin layer over the basin liner. The still was placed at the same level of the solar pond. Fig. 33 shows the schematic of the solar still coupled with shallow solar pond. The energy balance equations for upper glass cover, lower glass cover, basin liner, pond water and heat exchanger tube–heat exchanger fluid assembly are formulated, respectively, as follows: IðtÞh αg Ag þ hc;gl  gu Ag ðT gl  T gu Þ þ hr;gl  gu Ag ðT gl  T gu Þ ¼ hc;gu  a Ag ðT gu T a Þ þ hr;gu  a Ag ðT gu  T sky Þ

ð261Þ

IðtÞh τg αg Ag þ hc;fw  gl Aw ðT fw  T gl Þ ¼ hc;gl  gu Ag ðT gl T gu Þ þ hr;gl  gu Ag ðT gl T gu Þ

ð262Þ





IðtÞh τ2g τ0w αb Ab ðAhx =2Þ ¼ hw Ab  ðAhx =2Þ ðT b T fw Þ þ U b Ab ðT b  T a Þ

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Fig. 29. Flat plate collector assisted solar still [37].

Fig. 31. Schematic of modified solar still with parabolic trough concentrator [38].

IðtÞh αg Ag þ ht;w  g Aw ðT fw  T g Þ ¼ hc;g  a Ag ðT g  T a Þ þ hr;g  a Ag ðT g  T sky Þ

ð269Þ

Fig. 30. Concentrator assisted solar still [37].


¼ hc;gu  a Ag ðT gu  T a Þ þ hr;gu  a Ag ðT gu  T sky Þ þ Q u Þhx;fw

ð263Þ



IðtÞh τ2g αw Aw þ hw Ab ðAhx =2Þ ðT b  T fw Þ ¼ M fw C w ðdT fw =dtÞ

Numerical calculations were carried out by assuming the temperatures of the various components of the system are equal to the ambient temperature at t ¼0. From the numerical analysis, it was found that the daily efficiency of the solar still coupled with shallow solar pond is 54.98% higher than that obtained by still alone. Also it was suggested that the present system may be used as a source of hot water requirement for domestic applications in addition to the fresh water production. The results proved that coupling of the shallow solar pond, under the close mode of operation, to a single basin solar still significantly enhances the productivity and efficiency of the still all year round.

þ hc;w  gl Aw ðT fw  T gl Þ þ hc;fw  hxf ðAhx =2ÞðT fw  T hxf Þ þ U ss Ass ðT fw  T a Þ

ð264Þ

ðphx =2ÞIðtÞh τ2g τ0w αhx dx þ hc;b  hxf ðphx =2ÞðT b  T hxf Þdx þ hc;fw  hxf ðphx =2ÞðT fw  T hxf Þdx _ hxf C w ð∂T hxf =∂xÞdx þ Ahx ρw C w ð∂T hxf =∂tÞdx ¼m

ð265Þ

The rate of thermal energy transfer from the pond water to the heat exchanger’s fluid (Qu)hx,fw is calculated by using the following relation:

_ hxf C w ðT hxf Þout  ðT hxf Þin ðQ u Þhx;fw ¼ m ð266Þ It was observed that the annual average values of daily productivity and efficiency of the still with shallow solar pond were found to be higher than those obtained without shallow solar pond by 52.36% and 43.8%, respectively. The best performance of the active solar still with water feeding from the shallow solar pond could be achieved when the water mass flow rate equals 0.0009 kg/s, water thickness equals 0.03 m and with the heat exchanger diameter and length of 0.02 m and 5 m, respectively. Also it was found that the deviation between the estimated values of productivity by the proposed model with the experimental results is about 4%. El-Sebaii et al. [41] conducted another performance analysis to enhance the productivity of single basin solar still, especially during night time, by integrating a shallow solar pond, a heat exchanger and storage tank with the still as shown in Fig. 34. The energy balance equations for basin liner, elemental water length, and glass cover are given as follows: IðtÞh τg τw αb Ab ¼ hw Ab ðT b T fw Þ þ U b Ab ðT b  T a Þ IðtÞh τg αw bdx þ hw ðT b T fw Þbdx ¼ ht;w  g ðT fw  T g Þbdx     ∂T fw ∂T fw _ w dx þ ρw dw C w bdx þ mC ∂x ∂t

7.2.5. Heat pump Halima et al [42] developed a theoretical model to study the performance of a simple solar still coupled to a compression heat pump. The compression heat pump is made up of a condenser immersed in the water basin, evaporator located below the upper region of the glass cover, compressor and expander. The condenser will contribute to heat basin water, and thus its evaporation, during day time and especially during periods of low irradiation by the refrigerant (R134a) flowing through the heat pump. On the other hand, the evaporator will condense a large part of the water vapor. The water in the basin is heated by the incident solar radiation transmitted through the transparent glass cover and the condenser. Some of the water will evaporate and condense under the glass and the evaporator. Then, the condensate will be recovered by two collectors. Fig. 35 shows the schematic of the modified still. The energy balance for the glass cover is given by mg C g

dT g ¼ ð1  Rg Þαg IðtÞh þ ðqc;w  g þ qe;w  g þqr;w  g Þ qr;g  a  qc;g  a dt ð270Þ

The energy balance for the evaporator is given by mev C ev

dT ev ¼ qc;w  ev þ qe;w  ev  qe;ref dt

ð271Þ

The energy balance for the basin water is given by mw C w

ð267Þ

dT w ¼ ð1 Rg Þð1  αg Þαw IðtÞh  ðqc;w  g dt Ag W þ qe;w  g þ qr;w  g Þ þ qw þ Aw Aw

ð272Þ

The energy balance for the absorber is given by ð268Þ

mb C b

dT b ¼ ð1  Rg Þð1  αg Þð1  αw Þαb IðtÞh  qw qloss dt

ð273Þ

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885

Fig. 32. Schematic of solar pond assisted solar still [39].

The condensation rate is given by dmew Aw qe;w  g þ Aev qe;w  ev ¼ dt Aw hfg

ð274Þ

A computer simulation program based on the energy and mass balance equations was developed to investigate the performance of the solar still and the effect of the various design as well as the operating parameters that affect productivity. In this simulation program, energy and mass balance equations were solved simultaneously by using the fourth order Runge–Kutta method. The initial temperatures values of the system components were assumed to be approximately equal to ambient temperature. The solar still coupled with compression heat pump has the advantages of increasing water temperature by the condenser immersed in the basin water and enhancing the condensation surface area by the evaporator. From the numerical analysis, it was found that the productivity of the modified still is 75% higher than that of the conventional type. Also the effect of insulation type is marginal on the productivity, but the effect due to absorption coefficient is quite significant. The daily production is inversely proportional to the thickness of water. The proposed model was validated with the experimental data and a good correlation between predicted and experimental values was observed. The relative error between the theoretical and experimental results did not exceed 20%.

7.2.6. Hybrid PV/T Kumar and Tiwari [43] presented a model to estimate the internal heat transfer coefficients of a deep basin hybrid (PV/T) active solar still based on outdoor experimental observations. The internal heat transfer coefficients were evaluated by using thermal models developed by various researchers over the years. The hourly distillate outputs predicted by various thermal models have been compared by determining coefficient of correlation (r) and percentage deviation (ei). The schematic of the proposed system is shown in Fig. 36. Dunkle’s model, Chen et al. model, Adhikari et al. model, Zheng et al. model, and Kumar and Tiwari model were used during the analysis. These thermal models were used to estimate the internal heat transfer coefficients during computer simulation. The observed values of water temperature, inner glass temperature and distillate yield were used as an input at 100% relative humidity inside during the computation. It was inferred from the calculation that on the basis of hourly yield Kumar and Tiwari model is superior to the other models because of least percentage deviation except in extreme cases. It was found that the respective average values of convective and evaporative heat transfer coefficient of the hybrid active solar still are 3 and 5 times higher than the

Fig. 33. Schematic of single basin single slope solar still coupled with shallow solar pond [40].

passive solar still. The average annual values of convective heat transfer coefficient for the passive and hybrid (PV/T) active solar still were observed as 0.78 and 2.41 W/m2 K, respectively at 0.05 m water depth. Also the values of C and n differ for each design of the solar still and for the operating temperature range. Therefore, it was recommended that before predicting the performance theoretically, experiments must be carried out for given climatic conditions to evaluate the values of C and n for a particular design of solar still. Kumar et al. [44] developed a simple empirical model to estimate the glass cover temperature for the known values of water and ambient temperatures in a basin type hybrid (PV/T) active solar still (Fig. 37). The non-linear correlation for total internal heat transfer coefficient and linear correlations for external radiative heat transfer coefficient were developed on the basis of outdoor experimental results. Two flat plate collectors were integrated to the basin of the solar still by using insulated pipes to avoid thermal losses from the hot water in the pipe to the ambient. A photovoltaic (PV/T) module was integrated with one of the collector at its bottom, at entry to feed water at low temperature. The PV/T module was used to run a DC pump installed between solar still and the collector to circulate the water through collector under forced circulation mode. The energy balance for the hybrid (PV/T) active solar still is described as follows: The energy balance for the basin water is given by

α0w IðtÞs þ qw þ Q u ¼ mw C w

dT w þ qc;w  g þqe;w  g þ qr;w  g dt

ð275Þ

The energy balance for the glass cover is given by

α

0 g IðtÞs Ag þ ðqc;w  g þ qe;w  g þ qr;w  g Þ ¼ ðqr;g  a þ qc;g  a ÞAg

ð276Þ

The energy balance for the basin liner is given by

α0b IðtÞs ¼ qw þ qb þ qb ðAss =Ab Þ

ð277Þ

The rate of thermal energy feed from PV/T integrated flat plate collectors to the solar still is estimated by using the following equation: h Q u ¼ Am F R;m hp2 ðατÞm;eff ð1 K 1 Þ þ AC1 F R;C1 ðατÞC1;eff ð1  K 2 Þ i þ AC2 F R;C2 ðατÞC2;eff IðtÞC  Am F R;m U L;m ð1 K 1 Þ þ AC1 F R;C1 U L;C1 ð1  K 2 Þ

þ AC2 F R;C2 U L;C2 ðT wi1  T a Þ

ð278Þ

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Fig. 35. Schematic of the solar still coupled with compression heat pump [42].

Water mass: Fig. 34. Schematic of active solar still coupled with a shallow solar pond and a storage water tank [41].

α

AC1 F R;C1 U L;C1 AC2 F R;C2 U L;C2 AC1 F R;C1 U L;C1 AC2 F R;C2 U L;C2 þ  _ w Cw _ w Cw m m _ w C w Þ2 ðm ð279Þ AC2 F R;C2 U L;C2 _ w Cw m

ð280Þ

hp1 ¼

hc;c  pl Penalty factor because of glass cover U t;c  a þhc;c  pl

ð281Þ

hp2 ¼

hc;pl  w Penalty factor because of black surface U L1 þhc;pl  w

ð282Þ

K2 ¼

The glass cover temperature of the solar still is derived as Tg ¼

dT w þ ht;w  gi ðT w  T gi Þ dt

ð286Þ

Basin liner:

where K1 ¼

α0w IðtÞs þ hw ðT b  T w Þ þQ u ¼ mw C w

ð2991:684  19:84T w þ 0:033T 2w ÞT w þ Ar hw T a þ Ar ð0:141T a  36:026ÞT sky

ð283Þ where ð284Þ

For the known values of water temperature, ambient temperature, wind heat transfer coefficient and area ratio (Ag/Ab) of the still, the various heat transfer coefficients can be estimated after evaluating the glass cover temperature for hybrid (PV/T) active solar still. From the numerical solution, it was observed that the maximum relative error that occurs to predict the glass cover temperature is 1.12% in hybrid (PV/T) active solar still. The evaporative part of fractional energy utilized to evaporate the water within the still and responsible for distillate yield was predicted statistically to a level of r ¼ 0.99 and the computed maximum error of 1.2% were obtained between proposed and numerical results. Dev and Tiwari [45] established characteristic equation of hybrid (PV–T) active solar still based on annual experimental observations by using two methods. In the first method, linear and non-linear curves were plotted for both instantaneous gain efficiency and instantaneous loss efficiency. In the second method, characteristic equation for solar still was obtained using the matrix method. The energy balance equations of the hybrid (PV/T) active solar still are given as follows: Glass cover:

α0g IðtÞs þ ht;w  gi ðT w  T gi Þ ¼ ht;gi  a ðT gi  T a Þ

¼ hw ðT b  T w Þ þ hb ðT b  T a Þ

ð287Þ

The rate of useful heat gain from two flat plate collector with a photovoltaic module to the solar still basin water is given as:     AC F R;C U L;C Q u ¼ Am F R;m hp2 ðατÞm;eff 1  þ AC F R;C ðατÞC;eff IðtÞC mw C w     AC F R;C U L;C þ AC F R;C U L;C ðT wi1  T a Þ ð288Þ  Am F R;m U L;m 1  mw C w The characteristic equations developed by the first method with coefficient of correlation and root mean square percentage error are given as follows: Linear characteristic equation: y1 ¼ 0:1143 þ 5:4742x; ðr ¼ 0:9885; e ¼ 8:5Þ

ð289Þ

y2 ¼ 0:5913  9:1092x; ðr ¼ 0:8853; e ¼ 390:3Þ

ð290Þ

Non-linear characteristic equation:

ð2991:684  19:84T w þ 0:033T 2w Þ þ Ar hw þ Ar ð0:141T a  36:026Þ

Ar ¼ Ag =Ab

0 b IðtÞs

ð285Þ

y1 ¼ 0:1803 þ 8:6163x  34:123x2 ; ðr ¼ 0:9948; e ¼ 9:5Þ

ð291Þ

y2 ¼ 1:0644  31:622x þ 244:49x2 ; ðr ¼ 0:9887; e ¼ 10:4Þ

ð292Þ

where ð293Þ x ¼ ðT w  T a Þ=IðtÞ In the above expressions, y1 and y2 are the instantaneous gain and loss efficiencies, respectively. The characteristic equations developed by the second method with coefficient of correlation and root mean square percentage error are given as follows: 



n

o

ηiG ¼  0:0229  0:1717 ðT w  T a Þ=IðtÞ þ 0:1147 ðT w  T a Þ2 =IðtÞ ; ðe ¼ 7:4Þ ð294Þ n o   ηiL ¼  0:0548 þ 24:0557 ðT w  T a Þ=IðtÞ  0:6739 ðT w  T a Þ2 =IðtÞ ; ðe ¼ 4:0Þ

ð295Þ where, ηiG and ηiL are the instantaneous gain and loss efficiencies, respectively. It was observed that non-linear characteristic equations derived from the second method have low root mean square percentage error in comparison with the first method. But on the basis of monthly performance of the solar still, the characteristic equations derived from the first method are having less RMS percentage values. Hence the characteristic equations derived from the first method are recommended for thermal testing of hybrid PV–T active solar still. It was concluded that the non-linear characteristic equations better accommodates the operational

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887

Fig. 37. Schematic of a hybrid (PV/T) active solar still [44]. Fig. 36. Schematic of a hybrid (PV/T) active solar still [43].

behavior of the solar still coupled with flat plate collector and PV– T module. Boubekri et al. [46] studied the productivity of a single basin single slope solar still fitted with two reflectors coupled with a photovoltaic/thermal solar water heater system. To improve the productivity of the solar still, two methods were considered, either the use of plane reflectors in order to increase the solar flux during the sunshine period or by the storage of solar energy in the form of hot water using a storage tank that will supply the still with the hot water during the nocturnal period. The system consists of a conventional still with a hybrid PV/T collector and internal and external reflectors as shown in Fig. 38. The electric power generated by the hybrid PV/T solar collector enables the active still to operate within a forced circulation mode by the use of a mechanical pump. The use of reflectors aims to increase the solar radiation absorbed by the still. The PV/T solar water heater system (Fig. 39) used for supplying the still with hot water during the nocturnal period is made up of a storage tank connected to the hybrid PV/T collector. An electrical system constituting of a photovoltaic generator and ohmic heating resistances is used to increase the temperature of the water in the tank. In the energy balance equation, the rate of solar radiation reflected by the internal and external reflectors and absorbed by the glass, water, and basin liner have been introduced. The energy balance for the glass cover of the still is given by ðLg ρg C g Þ

∂T g þ qc;g  a þ qr;g  sky ¼ qe;w  g þ qc;w  g þ qr;w  g þ qg  ext þ IðtÞh αg ∂t

ð296Þ

where qg  ext is the rate of solar radiation reflected by the external reflector and absorbed by the glass. The energy balance for the water in the basin of the still is given by ðdw ρw C w Þ

∂T w þ qe;w  g þ qc;w  g þ qr;w  g ¼ qcd;w  b þ Q c  s þ Q st  s þ qw  ext ∂t

þ qw 

int þ IðtÞh

αw τ g

ð297Þ

where, Qc  s and Qst  s are the quantities of heat exchanged between the collector–solar still and storage tank–solar still systems, respectively; qw  ext and qw  int are the rates of solar radiation reflected by external and internal reflectors and absorbed by the water, respectively. The energy balance for the basin liner of the still is given by ðLb ρb C b Þ

∂T b þ qw þ qc;b  ins ¼ qb  ext þ qb  ∂t

int þIðtÞh αb τ g τ w

ð298Þ

where qb  ext and qb  int are the rates of solar radiation reflected by the external and internal reflectors and absorbed by the basin liner, respectively; qc,b  ins is the quantity of heat exchanged by conduction between the basin liner and the insulation.

The energy balance for the insulation of the still is given by ðLins ρins C ins Þ

∂T ins þqc;ins  a þ qr;ins  grd ¼ qc;b  ins ∂t

ð299Þ

where qc,ins a and qr,ins grd are the quantity of heat exchanged between the insulation–ambient and insulation–ground, respectively The rate of solar radiation reflected by the external reflector and absorbed by water (qw  ext) is given by the expression:   cos φ 1 sin φ qw  ext ¼ IðtÞdr τg ρext αw lm ð300Þ b  lm 2 tan ϕ tan ϕ The solar radiation reflected by the external reflector and absorbed by the glass (qg  ext) and by the absorber (qb  ext) is given as follows: qg  ext ¼

 αg
q =τ αw w  ext g

ð301Þ

qb  ext ¼

 αb
q =τ αw w  ext w

ð302Þ

The rate of solar radiation reflected by the internal reflector and absorbed by the water (qw  int) and by the absorber (qb  int) is given as: qw 

int

¼ IðtÞdr τg ρint αw lb tan θ

qb 

int

¼

αb
q αw w 

τ

int w



cos φ tan ϕ

ð303Þ ð304Þ

From the numerical simulation of the active still, it was observed that the addition of reflectors improved the daily production of the still about 127.06% in winter, 21.78% in spring and 10.1% in summer. Also the coupling of the still with a thermal storage tank led to an increase of the production rate equal to 17.36%, 28.34% and 33% respectively for winter, spring and summer. The daily production rate of the still coupled with the photovoltaic/thermal system was about 47.61% in winter, 137.5% in spring and 131.06% in summer. It was concluded that the effect of the reflectors on the increase of the daily production of the still is very significant during the period of winter compared to the spring and summer but on the other hand, the storage tank is far more important in spring and summer in comparison with winter. 7.2.7. Key findings and discussion on thermal models of active solar still To improve the performance of the solar still, many active methods were invented by the researchers over the years. Many research works have been reported on active solar still with flat plate collector, concentrating collector, evacuated tube collector, heat pipe, and hybrid photovoltaic/thermal system, etc. In active

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solar stills, the quantity of additional thermal energy supplied to the basin water is included during its thermal analysis. From the literature, it is found that the well-known Dunkle’s model is best suited to determine internal heat transfer coefficients for only lower water depths (0.01–0.03 m) and for lower operating temperature ranges (o50 1C). But there is a marginal variation in the values of convective and evaporative heat transfer coefficients with the increase in water depth and the correlations need modification for higher Grashof numbers. The Dunkle’s model is effective only for the passive solar stills which operate under relatively lower water temperature range. The active solar still system is generally termed as a high temperature distillation system which operates 480 1C depending upon the type of solar collector coupled with solar still. On the basis of hourly yield, for high temperature range, Kumar and Tiwari model (KTM) is superior to other models under consideration with least percentage deviation except in extreme cases. The values of C and n in Nusselt expression differ for each design of the solar still and for the operating water temperature range. Therefore, it is recommended that before predicting the performance theoretically, experiments must be carried out for given climatic conditions to evaluate the values of C and n for particular design of solar still. The KTM model to evaluate C and n is in close agreement with experimental results within the accuracy of 20%. Other models like Clark’s model, Zheng Hongfei et al.’s model, and Adhikari et al. model have not been exploited by the researchers due to their limitations and complexity. Tsilingiris model evaluated the thermo-physical properties of binary mixture of dry air and water–vapor, instead of improper dry air properties alone, to predict the convective and evaporative heat transfer coefficients as well as the distillate output in solar distillation systems. The linear and non-linear equations may be used for removing the chances of more errors to select the appropriate design of solar still. The performance of non-linear characteristic equation is better than linear characteristic equation for the estimation of still parameters. It is observed from the analyses that the performance of the active solar still with new technologies like evacuated tube collector, heat pipe, and hybrid PV/T system are better than the existing flat plate and concentrating collectors. However, the economic aspect of active solar stills must be analyzed before its implementation. The cost of additional thermal energy supplying equipment should be included to determine the payback period of the solar still. Also the operational and maintenance aspects of these devices must be analyzed for long term usage with the solar still due to high temperature applications. Based on the above discussion, it is concluded that the thermal model for active solar still may be developed based on Kumar and Tiwari model with incorporating binary mixtures of dry air and water–vapor properties on the basis of non-linear characteristic equations.

considered in the proposed mathematical model. Fig. 40 shows the schematic of the single basin double slope solar still with aluminium rectangular fin arranged in length wise and breadth wise directions in the basin covered with cotton and jute cloths. Light black cotton cloth, light jute cloth, sponge sheet, coir mate and waste cotton pieces were used as wick materials in the basin. A layer of water equivalent to 0.5 cm (about 7.5 kg of mass) was maintained in the still basin. The energy available for utilization by the still for a given instant is the sum of global solar radiation transmitted through the north and south side covers and given by Q τ ¼ Q τN þ Q τS

ð305Þ

where Q τN ¼ τN AgN IðtÞN

ð306Þ

Q τS ¼ τS AgS IðtÞS

ð307Þ

In the above expressions, τN and τS are the transmittance of the north and south side glass covers, respectively. The transient energy balance equation for the basin water is given by ðMw C w þ M wk C wk þ M fn C fn Þ

dT w ¼ Q τ αw  Q c;w  g  Q r;w  g  Q r;w  g  Q b  Q rw dt

ð308Þ The evaporated mass of water is continuously replaced and mass of water in the basin is maintained constant. The replaced water comes at ambient temperature and takes heat from the basin. The heat taken by the replaced water is given by Q rw ¼ mew C w ðT a  T w Þ

Fig. 38. Schematic of active solar still with reflectors and hybrid collector [46].

7.3. An assortment of new solar still designs This section describes the experimental work and corresponding modifications done on the thermal modeling for various innovative designs of solar stills. 7.3.1. Single basin double slope solar still Kalidasa Murugavel and Srithar [47] developed a theoretical model for a single basin double slope with minimum mass of water and different wick materials. Still with fin arranged in different configurations and covered with different wicks were also tested. The variation in transmittance of the cover was also

ð309Þ

Fig. 39. Schematic of PV/T solar water heater system [46].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

The transient energy balance equation for the glass cover is given by Mg C g

dT g ¼ αg Q i þ Q c;w  g þ Q r;w  g þ Q r;w  g  Q c;g  a  Q r;g  a dt ð310Þ

The refined thermal model used to accurately predict the production rate is given as mew ¼ 0:012ðT w T g ÞðT g  T a Þ  3:737 10  3 T w ðT g  T a Þ  5:144  10  3 T g ðT g  T a Þ þ 5:365 10  3 ðT g  T a Þ2 þ0:212ðT g T a Þ  3:828

depending upon various parameters associated with design, climatic and operational conditions. Dwivedi and Tiwari [49] developed thermal modeling of a double slope active solar still coupled with flat plate collector on the basis of energy balance of its various components under natural circulation mode. The thermal model was validated by experimental data. Fig. 42 shows the schematic of a flat plate collector coupled double slope solar still. The energy balances on east condensing cover are given as follows: Inner condensing cover

α0g IðtÞE þ htE;w  g ðT w  T giE Þ U EW ðT giE  T giW Þ ¼

10  3 T w ðT w T g Þ  5:015  10  3 T g ðT w  T g Þ þ 2:997

889

Kg ðT  T goE Þ Lg giE ð316Þ

10  3 ðT w T g Þ2 þ 0:217ðT w  T g Þ þ1:182  10  3 T w T g Outer condensing cover

þ1:663  10  3 T 2g  0:106T g 0:065T w þ8:352  10  4 T 2w þ 1:992

ð311Þ

Based on the analysis, it was observed that the light black cotton cloth was the most effective which yielded higher daily productivity. With the different fin configurations in the basin, the aluminium rectangular fin covered with cotton cloth and arranged in length wise direction was more effective and gave slightly higher production than the light black cotton cloth. The actual and theoretical values calculated using the proposed and Dunkle’s models were compared. It was found that, the various theoretical and actual parameters were varying in same pattern. But, the deviations between these parameters were higher. To predict the production rate accurately, the thermal model in terms of different temperatures was applied as a refinement for the proposed model. The estimated production rate using the refined model closely agreed with the experimental values. Dev et al. [48] obtained the characteristic equation with respect to a non-dimensional representative factor for a double slope passive solar still based on experimental data. These characteristic equations can be used for further modifications in the existing design of double slope passive solar still in terms of design, operating and climatic parameters. The schematic of the double slope solar still is shown in Fig. 41. The orientation of the solar still was kept east–west to receive solar radiation for maximum hours of sunshine. The following are the mathematical expressions of instantaneous gain and loss efficiencies of solar still, used for the analysis: The instantaneous gain efficiency is given as   ðT  T Þ=IðtÞ ηiG ¼ ðατÞeff þ U 0 : w a  ð312Þ ðT w  T a Þ=IðtÞ max where  

U 0 ¼ ðUAÞeff : ðT w  T a Þ=IðtÞ max The instantaneous loss efficiency is given as   ðT T Þ=IðtÞ ηiL ¼ ðατÞEFF  U″: w a  ðT w  T a Þ=IðtÞ max where  

U″ ¼ U L : ðT w  T a Þ=IðtÞ max

ð313Þ

ð314Þ

ð315Þ

The linear and non-linear characteristic curves were obtained using the above equations under quasi-steady state condition. It was found that non-linear characteristic curves show higher values of coefficient of correlations than that of linear characteristic curves. Also the non-linear characteristic curves have more accuracy to predict the performance of the solar still under quasisteady state condition. They can be used for analyzing the performance, thermal testing and further design modification

Kg ðT T goE Þ ¼ haE ðT goE T a Þ Lg giE

ð317Þ

The energy balances on west condensing cover are given as follows: Inner condensing cover

α0g IðtÞW þ htW;w  g ðT w  T giW Þ þ U EW ðT giE  T giW Þ ¼

Kg ðT  T goW Þ Lg giW ð318Þ

Outer condensing cover Kg ðT  T goW Þ ¼ haW ðT goW T a Þ Lg giW The energy balance for basin liner is given by


α0b IðtÞE þIðtÞW ¼ 2U bw ðT b  T w Þ þ 2U ba ðT b  T a Þ

ð319Þ

ð320Þ

The energy balance for water mass is given by mw C w


 dT w ¼ α0w IðtÞE þ IðtÞW þ 2U bw ðT b  T w Þ  htE;w  g ðT b  T giE Þ dt  htW;w  g ðT b  T giW Þ þ Q u ð321Þ

where



Q u ¼ AC F 0 ðατÞC IðtÞC  U LC ðT w T a Þ

ð322Þ

It was found that the double slope active solar still under natural circulation model gives 51% higher yield than the double slope passive solar still. But the thermal efficiency of double slope active solar still is lower than the thermal efficiency of double slope passive solar still. However, the exergy efficiency of double slope active solar still is higher than the exergy efficiency of double slope passive solar still. Rubio et al. [50] proposed a lumped parameters mathematical model to study the asymmetries that arise in the temperature and distillate yield in double slope solar stills. The condenser cover of a double slope solar still may be considered as a system having two thermally independent flat plates. The high inclination and opposite location of each one results in a different orientation with respect to the sun, and therefore the characteristics of absorbed and transmitted energy are different. The main heat flows in a double slope solar still is shown in Fig. 43. The energy balance equation of condensing cover 1 is given by C g1

dT g1 ¼ α0g1 IðtÞ þ U w  g1 ðT w  T g1 Þ  U g1  g2 ðT g1  T g2 Þ  U g1  a ðT g1  T a Þ dt

ð323Þ The energy balance equation of condensing cover 2 is given by C g2

dT g2 ¼ α0g2 IðtÞ þ U w  g2 ðT w  T g2 Þ  U g2  g1 ðT g2  T g1 Þ  U g2  a ðT g2  T a Þ dt

ð324Þ

890

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

 Ut ¼

Fig. 40. Schematic of single basin double slope solar still [47].

The energy balance equation for water mass is given as dT w ¼ α0w IðtÞ þ U w  b ðT b  T w Þ  U w  g1 ðT w  T g1 Þ  U w  g2 ðT w T g2 Þ Cw dt

ð325Þ The energy balance equation for basin liner is given as Cb

dT b ¼ α0b IðtÞ  U b  w ðT b  T w Þ  U b  a ðT b  T a Þ dt

ð326Þ

The equations were solved by Runge–Kutta method by feeding the recorded wind speed, ambient temperature and solar radiation to the model. It was found that the predicted temperature differences between the two covers of the double slope solar still are slightly underestimated by the model, probably resulting from the complexity of the dynamical effects produced by external environmental factors. But the overall results show a good correlation between the predictions and experimentation. It is concluded that the Dunkle’s model is the option to study the operation of a still, and can be extended to show the detailed thermal performance of double slope cover systems. Singh et al. [51] attempted to optimize the orientation of the glass cover inclination of the double slope solar still to achieve higher yield. The effect of water depth on the hourly instantaneous cumulative and overall thermal efficiency and internal heat transfer coefficient was also investigated. Fig. 44 shows the cross sectional view of a double slope solar still with design parameters. The energy balance equations for each component of the still are as follows: Glass cover: Ab ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g  T a ÞAg

ð327Þ

Water mass: ðατÞw IðtÞs Ag þ hw ðT b  T w ÞAb þQ u ¼ M w C w

dT w þ ht;w  g ðT w  T g ÞAb dt ð328Þ

Basin liner:

ðατÞb IðtÞs Ag ¼ hw ðT b T w Þ þ hb ðT b T a Þ Ab

1

ht;w  g

þ

1 ht;g  a secθ

1

Based on the numerical computations, it was found that the solar still gives the maximum yield for an east–west orientation for θ o551, during the winter period. For lower depth of water, the hourly variation of yield is similar to those of solar intensity due to negligible thermal capacity. The instantaneous thermal efficiency increases with an increase of inclination due to the increase of solar radiation on the inclined surface for the winter condition. But the instantaneous thermal efficiency decreases with an increase of water depth because most of the thermal energy is not utilized for evaporation and stored in the water mass itself. Also the cumulative efficiency becomes constant after reaching a steady state condition. Mowla and Karimi [52] developed a mathematical model for double slope solar still shown in Fig. 45 and calculated the rate of production of fresh water from sea water as a function of different meteorological parameters and the solar still specifications. The results obtained from the numerical computations were validated by the experimental data. The energy balance for glass cover, water mass and basin liner are expressed as follows, respectively: ht;w  g ðT w  T g Þ ¼ ht;g  a F 1 ðT g  T a Þ

ρw U dw U C w

dT w ¼ α0w IðtÞs  ht;w  g ðT w  T g Þ  hw F 2 ðT w  T b Þ dt

α0b IðtÞ ¼ hw F 2 ðT b  T w Þ þ U ss F 3 ðT b T a Þ þ U b ðT b  T a Þ

ðht;w  g T w Þ þ T a ht;g  a secθÞ ht;w  g þ ht;g  a secθ

The instantaneous thermal efficiency is expressed as   h h secθ ðατÞeff T w0 T a  at ηi ¼ e;w  g t;g  a ð1  e  at Þ þ e IðtÞs ht;w  g þ ht;g  a secθ U t þ U b where

 ðατÞeff ¼ ðατÞw þ ðατÞb

 hw secθ hw þ hb

ð329Þ

ð330Þ

ð331Þ

ð332Þ

ð334Þ

ð335Þ

ð336Þ

where F1, F2 and F3 are glass area correction factor (Ag/Ab), still area correction factor (As/Ab), and side wall area correction factor (Ass/ Ab), respectively. From the study, it was found that the mathematical model overestimates of about 5.1% for the rate of distilled water production. This discrepancy could be explained by some experimental errors such as some distilled water drops falling back into the basin water, or the use of horizontal solar radiation for the glass cover while it is partially inclined. Also the rate of water production increases when the water depth in the basin is decreased. Sartori [53] presented a theoretical comparison between the thermal behaviors of a basin type solar still and an open type solar evaporator. The temperatures and the heat and mass transfer rates in the transient mode as well as parametric representations from both the systems were obtained and compared. Figs. 46 and 47 show the energy balance in both solar still and solar evaporator, respectively.

The glass cover temperature is expressed as Tg ¼

ð333Þ

Fig. 41. Schematic of double slope passive solar still [48].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

891

regenerative solar still was mathematically modeled by writing energy balance equation for each of the system components, namely; basin, water in basin, first glass cover, water film on top of first glass cover, and second glass cover. The schematic of the regenerative solar still is shown in Fig. 48. It consists of two basins (effects), where the latent heat of condensation released to the first glass cover was utilized to produce additional fresh water from a second effect. The second effect may be arranged in such a way that can have either a flowing water film or a stationary one of larger thickness. The absorptivity of water in both effects was included in the energy balance equations and accounted for in the simulations. The energy balance equations for the system components are as follows: First effect basin liner (b): mb C b

dT b ¼ IðtÞs Ab  qw  qloss dt

ð344Þ

Water in the first effect (w): mw C w

mg C g The energy balance in transient mode for the solar still is formulated as dT w dt

ð337Þ

where

dT g1 ¼ IðtÞs Ag1 þ qr;w  g1 þ qc;w  g1 þ qe;w  g1  qc;g1  wf dt

ð346Þ

Water in the second effect (wf): mwf C w

dT wf ∂T _ wf C w wf dx  qc;wf  g2  qr;wf  g2  qe;wf  g2 ¼ IðtÞs Awf þ qc;g1  wf  m dt ∂x

ð347Þ Upper glass (g2):

qkw ¼ kbs ðT w  T a Þ

ð338Þ

In the above expression, kbs is determined through the overall heat transfer coefficient for a multilayer wall. The heat transfer between the water and the glass is given by the heat transfer rates by radiation, convection and evaporation whereas the heat flux to the ambient is the summation of such quantities plus the solar energy absorbed by the cover, i.e. qga F 1 ¼ qr;w  g þ qc;w  g þ qe;w  g þ αg IðtÞh

ð339Þ

The internal heat transfer rates between water and glass cover (qrw, qcw and qew) were calculated by Dunkle’s relations. The energy balance for the solar evaporator is formulated as

αw IðtÞ ¼ qrw þ qcw þ qkw þ C ev

ð345Þ

Lower glass (g1):

Fig. 42. Schematic of double slope active solar still [49].

αg IðtÞh þ αw τg IðtÞh ¼ qga F 1 þ qkw þ C s

dT w ¼ IðtÞs Aw þ qw  qr;w  g1  qc;w  g1  qe;w  g1 dt

dT w dt

ð340Þ

where

h i qrw ¼ εw σ ðT w þ 273:15Þ4  ðT sky þ 273:15Þ4

ð341Þ

qcw ¼ 39:183  10  1 v0:5 ðT w  T a Þ

ð342Þ

qew ¼ 26:639  10  1 v0:5 ðP w  P d Þhfg =P a

ð343Þ

mg C g

dT g2 ¼ IðtÞs Ag2 þ qc;wf  g2 þ qr;wf  g2 þ qe;wf  g2  qr;g2  sky  qc;g2  a dt

ð348Þ Total condensation rate: dmew he;w  g1 ðT w  T g1 Þ he;wf  g2 ðT wf  T g1 Þ ¼ þ ðhfg ÞT wf dt ðhfg ÞT w

It was found that the productivity of the regenerative still is about 20% higher than that for the conventional still. Making the stills perfectly insulated increases their productivity two and one half folds. There is more positive effect due to insulation on the regenerative still compared with the conventional still. The wind speed has a significant effect on the productivity; it can increase the productivity of the still by more than 50% if the wind speed increased from 0 to 10 m/s. Also the thickness of water on top of the first glass cover and the mass flow rate of water going into the second effect have marginal effect on the productivity of the regenerative still. El-Sebaii [55] presented a transient mathematical model for a triple basin solar still. The energy balance equations for various elements were solved analytically and the performance of the

From the numerical calculations, it was inferred that the evaporation in the solar still is much lesser than that in open evaporator despite the higher water temperatures in the former system. This is also true even when the water temperature of both systems is the same. The evaporation is the major heat loss in both solar still and solar evaporator and is larger than the other three modes together (radiation, conduction and convection). 7.3.2. Multi-basin solar still Zurigat et al. [54] evaluated the performance of a regenerative desalination unit which consists of two basins with provision for cooling water to flow in and out of the second effect. The

ð349Þ

Fig. 43. Heat flows in a double slope solar still [50].

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overnight. Also the total daily productivity of the system is a maximum for the least water masses in the lower and middle basins without dry spots over the base of each effect. The total daily productivity of the triple basin solar still is found to increase with an increase of wind speed until a typical velocity (vt). Hence it is recommended to build multi effect solar stills in windy places or to use artificial sources of wind running at vt. Al Baharna et al. [56] presented the performance analysis of a triple basin solar still integrated with a solar water heater. Different area ratios between the solar still and the solar water heater were also investigated. The schematic of the triple basin solar still integrated with a solar water heater is shown in Fig. 50. The system was analyzed by presenting energy balance equations of the solar still and solar water heater. In this analysis, basins were numbered from upper to lower in ascending order. The energy balance equations for the upper cover, inner glass covers and the absorber plate of the solar still, respectively, are presented as:

Fig. 44. Cross sectional view of a double slope solar still [51].

system was investigated by computer simulation. The effect of water mass in each basin of the still and the wind speed on the daily productivity of the system were investigated. Fig. 49 shows the schematic diagram of the triple basin solar still. In the triple basin solar still, two glass sheets were fixed in between the basin liner and the glass cover of the single basin still. These glass sheets served as the base of extra shallow depths of saline water, and the whole assembly behaved as three simple basin solar stills placed one above the other. The water in the middle and upper basins makes use of the latent heat from condensation released at the inner surfaces of the glass covers of the lower and middle basins, respectively. The total productivity of the system is the sum of the productivities of the individual basins. During this analysis, the basins were numbered from lower to upper in ascending order. The energy balance equations for the various components of the system are expressed as follows: Basin liner: IðtÞb ¼ hw ðT b  T w1 Þ þU b ðT b  T a Þ

IðtÞg1 þ ht;w1  g1 ðT w1  T g1 Þ ¼ hr;g  a ðT g1  T sky Þ þ hc;g  a ðT g1  T a Þ ð357Þ IðtÞg2 þ ht;w2  g2 ðT w2  T g2 Þ ¼ hc;g2  w1 ðT g2 T w1 Þ

ð358Þ

IðtÞg3 þ ht;w3  g3 ðT w3  T g3 Þ ¼ hc;g3  w2 ðT g3 T w2 Þ

ð359Þ

IðtÞb ¼ hw ðT b  T w3 Þ þ U b ðT b T a Þ

ð360Þ

where IðtÞg1 ¼ αg IðtÞs

IðtÞg2 ¼ αg τg τw1 IðtÞs

IðtÞg3 ¼ αg τ2g τw1 τw2 IðtÞs

IðtÞb ¼ αb τ3g τw1 τw2 τw3 IðtÞs

The energy balance equations for the water masses in the three basins of the solar still are given as: IðtÞw1 þ hc;g2  w1 ðT g2  T w1 Þ þ d=dtðmd1 C w T a =Ab Þ M w1 C w dT w1 ¼ ht;w1  g1 ðT w1  T g1 Þ þ Ab dt

ð350Þ

Water mass in the lower basin: IðtÞw1 þ hw ðT b  T w1 Þ ¼

M w1 C w dT w1 þ ht;w1  g1 ðT w1  T g1 Þ Ab dt

ð351Þ

Lower glass cover: IðtÞg1 þht;w1  g1 ðT w1  T g1 Þ ¼ hc;g1  w2 ðT g1  T w2 Þ

ð352Þ

Water mass in the middle basin: IðtÞw2 þ hc;g1  w2 ðT g1  T w2 Þ ¼

M w2 C w dT w2 þht;w2  g2 ðT w2  T g2 Þ Ab dt ð353Þ

Fig. 45. A typical single basin double slope solar still [52].

Middle glass cover: IðtÞg2 þht;w2  g2 ðT w2  T g2 Þ ¼ hc;g2  w3 ðT g2  T w3 Þ

ð354Þ

Water mass in the upper basin: IðtÞw3 þ hc;g2  w3 ðT g2  T w3 Þ ¼

M w3 C w dT w3 þht;w3  g3 ðT w3  T g3 Þ Ab dt ð355Þ

Upper glass cover: IðtÞg3 þht;w3  g3 ðT w3  T g3 Þ ¼ hr;g  a ðT g3 T sky Þ þ hc;g  a ðT g3  T a Þ ð356Þ From the numerical investigations, it was found that the productivity of the lower basin (first effect) is higher than the productivities of the middle (second effect) and upper (third effect) basins during the daytime, and this behavior is reversed

Fig. 46. Energy balance for the solar still [53].

ð361Þ

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

893

Fig. 47. Energy balance for the solar evaporator [53].

IðtÞw2 þ hc;g3  w2 ðT g3  T w2 Þ þ d=dtðmd2 C w T a =Ab Þ M w2 C w dT w2 ¼ ht;w2  g2 ðT w2  T g2 Þ þ Ab dt

Fig. 48. Schematic of the regenerative solar still [54].

ð362Þ

_ w C w ðT wi  T wo Þ=Ab IðtÞw3 þ hw ðT b  T w3 Þ þ d=dtðmd3 C w T a =As Þ þ m M w3 C w dT w3 ð363Þ ¼ ht;w3  g3 ðT w3  T g3 Þ þ Ab dt where IðtÞw1 ¼ αw1 τg IðtÞs

IðtÞw2 ¼ αw2 τ2g τw1 IðtÞs

IðtÞw3 ¼ αw3 τ3g τw1 τw2 IðtÞs

The energy balance equations for various nodes of the solar water heater were also used along with the above equations to study the performance of the proposed still. From the transient analysis, it was found that the daily production rate increases considerably due to the multi basins in the still and augmentation of the solar water heater. The daily productivity of the still increased from 10.64 kg/day to 24.48 kg/day when the area ratio of solar water heater to the still is unity. Although the daily productivity increases with increasing the area of the water heater, the maximum percentage improvement is obtained when equal areas of the solar still and water heater are used. 7.3.3. Double basin double slope solar still Rajaseenivasan and Kalidasa Murugavel [57] presented theoretical models for single basin double slope and double basin double slope solar stills. The effect of varying water mass in both upper and lower basin on productivity of the double basin double slope still was investigated and the results were compared with the single basin still. Fig. 51 shows the schematics of both single and double basin double slope solar stills with design parameters. The energy balance equations of double basin double slope solar still are given as follows: Basin liner:   dT Ab  ABb  IðtÞs ¼ mb  C b  b þQ c;b  w þQ loss ð364Þ dt Water mass in the lower basin: ðAw;l  ABw;l  IðtÞs Þ þ Q c;b  w   dT w ¼ mw  C w  þ Q c;w  g;l þ Q r;w  g;l þ Q e;w  g;l dt l

ð365Þ

Lower glass cover: ðAg;l  ABg;l  IðtÞs Þ þQ c;w  g;l þ Q r;w  g;l þ Q e;w  g;l   dT g ¼ mg  C g  þ Q c;g  w;u dt l

ð366Þ

Water mass in the upper basin: ðAw;u  ABw;u  IðtÞs Þ þ Q c;g  w;u   dT w ¼ mw  C w  þ Q c;w  g;u þ Q r;w  g;u þ Q e;w  g;u dt u Upper glass cover: ðAg;u  ABg;u  IðtÞs Þ þ Q c;w  g;u þ Q r;w  g;u þ Q e;w  g;u

ð367Þ

¼ mg  C g 

  dT g þ Q r;g  sky þ Q c;g  a dt u

ð368Þ

The energy balance equations of single basin double slope solar still are given as follows: Basin liner:   dT Ab  ABb  IðtÞs ¼ mb  C b  b þ Q c;b  w þ Q loss ð369Þ dt Water mass: ðAw  ABw  IðtÞs Þ þ Q c;b  w   dT w þQ c;w  g þ Q r;w  g þ Q e;w  g ¼ mw  C w  dt

ð370Þ

Glass cover: ðAg  ABg  IðtÞs Þ þ Q c;w  g þ Q r;w  g þ Q e;w  g   dT g þ Q c;g  a þQ r;g  sky ¼ mg  C g  dt

ð371Þ

From the experimental and theoretical study, it was found that the production of the solar still increases with decrease of water mass in both and upper and lower basins. Also the lower basin production is higher than upper basin with reduced mass of water in lower basin. The double basin still production rate is higher than the single basin still around 85% for the same basin condition. The experimental analysis is agreed well with the theoretical results and the deviations between theoretical and experimental values were within 10%. 7.3.4. Multi-effect solar still Fath [58] presented a transient analysis of a single basin two effect solar distillation unit under passive mode of operation. The distillation unit consists of a second effect still connected to a single sloped solar still, of a movable shutter fashion type reflector back and located at its shaded side as shown in Fig. 52. The movable shutter reflector will maximize the reflected solar energy at different site locations and different seasons and allow purging the vapor. The second effect still acts as an additional heat and mass sink that sucks the evaporated water vapor from the first effect still. The purged vapor condenses and it’s sensible and latent heat is utilized to heat the basin water of the second effect for additional evaporation. Fig. 53 shows the energy balance in the proposed model. The energy balance equations for the distillation unit can be written as follows: First effect basin water: M w1 C w1 dT w1 =dt ¼ ðτg αw1 ÞIðtÞA Q e1  Q c1  Q r1  Q b1

ð372Þ

First effect glass cover: M g1 C g1 dT g1 =dt ¼ αg1 IðtÞA þ Q eg1 þ Q cg1 þ Q rg1  Q air1  Q sky1

ð373Þ

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Basin liner:

α0b IðtÞs ¼ hc;b  w ðT b  T w Þ þ hb ðT b  T a Þ

ð380Þ

where   Ar U LC Q u ¼ Aa F R ðατÞeff IðtÞC  ðT w  T a Þ Aa

Fig. 49. Schematic of triple-basin solar still [55].

Second effect basin water: M w2 C w2 dT w2 =dt ¼ Q e;1  2 þ Q c;1  2  Q b2  Q e2  Q c2  Q r2

ð374Þ

Second effect glass cover: M g2 C g2 dT g2 =dt ¼ Q eg2 þ Q cg2 þ Q r2  Q air2  Q sky2

ð375Þ

In the above expressions, Q represents the heat transfer rate between various components of the solar still. From the numerical computations, it was observed that the first to second effects volume ratio, the solar intensity, the base and side wall insulation, saline water initial temperature and ambient temperature significantly affect the still productivity. The overall distillation unit productivity was found to be 10.7 kg/ m2/day. Other parameters such as the reflectivity of the inner surface of the second effect cover, the first and second effect basins water masses, and wind speed were found to have less significant effect on the still productivity. Prasad and Tiwari [59] presented an analysis of a double effect active distillation unit incorporating the effect of climatic and design parameters. Based on the energy balance equations for each component of the distillation system, the hourly yield for each effect was evaluated and the results were compared with single effect distillation unit. The effect of flow velocity in the upper basin of the unit was also studied. The cross sectional view of the double effect distillation system coupled with a CPC collector under forced circulation mode is shown in Fig. 54. During the numerical analysis of the system, the lower basin was taken as 1 and upper basin was considered as 2. The energy balance equations for each component of the system, considering an elemental thickness of “dx” and width “b” for flowing water, are as follows: Upper glass cover: ht;fw  g2 ðT fw  T g2 Þbdx ¼ ht;g2  a ðT g2  T a Þbdx

ð381Þ

It was observed from the numerical computations that the temperature of water in the lower basin is increased in comparison with single effect distillation due to the reduced upward heat losses. But the hourly output in the lower basin is reduced due to the reduced temperature difference between the water and glass temperatures. However the overall output is increased due to reutilization of the latent heat of evaporation in the second effect. The hourly yield rate from lower basin is found to increase with increase of flow velocity of water due to the fast removal of latent heat of vaporization. But the total hourly yield and operating temperature are reduced by the high flow rate of water. It was concluded that the evaporative heat transfer coefficient is the strong function of the operating temperature range and the convective and radiative heat transfer coefficients do not vary significantly due to increase in flow rate of water. Kumar and Tiwari [60] developed a theoretical model for the prediction of the daily yield from an active double effect solar distillation unit. The latent heat of condensation was utilized for further distillation by flowing water over the lower condensing cover. The double effect solar still was coupled with a flat plate collector to supply additional thermal energy into the system. The effects of water depth, collector area, and flow rate on daily yield were also analyzed by numerical computations. Fig. 55 shows the

ð376Þ

Flowing water: _ fw C fw ht;g1  fw ðT g1  T fw Þbdx ¼ m

dT fw dx þht;fw  g2 ðT fw  T g2 Þbdx dt ð377Þ

Lower glass cover: ht;w  g1 ðT w  T g1 Þ ¼ ht;g1  f w ðT g1  T f w Þ

ð378Þ

Lower water mass: hc;b  w ðT b  T w Þ þ Q u ¼ M w C w

dT w þ ht;w  g1 ðT w  T g1 Þ dt

ð379Þ Fig. 50. Configuration of a triple basin still integrated with a solar water heater [56].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

schematic of water flowing over a glass cover of solar still coupled with the flat plate collector. The energy balance equations of the different components of the active solar still are as follows: Upper glass cover: ht;w2  g2 ðT w2  T g2 ÞAw2 ¼ ht;g2  a ðT g2  T a ÞAg2

ð382Þ

Flowing water: _ w2 C w2 ht;g1  w2 ðT g1 T w2 Þbdx ¼ m

dT w2 þht;w2  g2 ðT w2  T g2 Þbdx dx ð383Þ

Lower glass cover: ht;w1  g1 ðT w1  T g1 ÞAg1 ¼ ht;g1  w2 ðT g1  T w2 ÞAw2

ð384Þ

895

Kumar and Tiwari [61] evaluated the daily yields for multi effect active solar distillation systems by solving one-order coupled differential equations by Runge–Kutta method. The numerical computations were done for hourly variation of various temperatures, yield and overall thermal efficiency up to the fourth effect of the distillation unit. The predicted results were validated by an experimental setup of single effect with one collector connected with the basin. The multi effect solar distillation unit was coupled with a panel of flat plate collectors as shown in Fig. 56. The energy balance equations for each component of the system are as follows: Glass cover:

αgj IðtÞs Agj þ ht;wj  gj ðT wj  T gj ÞAwj ¼ ht;gj  wðj þ 1Þ ðT gj T wðj þ 1Þ ÞAgj ð387Þ

Lower water mass: ðατÞw1 IðtÞs Aw1 þ hc;b  w1 ðT b  T w1 ÞAb þ Q u dT w1 Aw1 þ ht;w1  g1 ðT w1 T g1 Þ þhb ðT w1  T a ÞAb ¼ M w1 C w1 dt

Water mass for j¼1: ð385Þ

¼ mw1 C w

Basin liner: ðατÞb IðtÞs ¼ hc;b  w1 ðT b T w1 Þ þ hb ðT b  T a Þ

ðατÞw1 IðtÞs Aw1 þ hc;b  w1 ðT b  T w1 ÞAb þ Q u

ð386Þ

It was observed from the numerical computations that the water and glass cover temperatures for the lower basin are higher than for the upper basin. Also the evaporative heat transfer coefficient in the lower basin is higher than in the upper basin due to the higher operating water temperature in the lower basin. But the convective and radiative heat transfer coefficients remain the same for the upper and lower basins. Hence it is inferred that the convective and radiative heat transfer coefficients are independent of the operating temperature range. Even though the latent heat of condensation is partially utilized for evaporation in the upper basin, the yield from the upper basin is much lower in comparison to the lower basin due to heat carried away by the flowing water. Also the daily yield increases with an increase of collector area, because the thermal energy in the basin increases as the collector area increases. But the rate of increase in daily yield decreases as the number of collectors increases and becomes zero after the number of collectors is greater than 12. The storage effect in the basin increases as the water depth increases, and hence, the overall water temperature decreases for a given amount of solar energy. Because of the low operating temperature, the rate of evaporation also decreases, and hence, the daily yield and thermal efficiency decrease. It was concluded that the yield is maximum at the optimized flow velocity of 1.8 m/s.

dT w1 þ ht;w1  g1 ðT w1  T g1 ÞAw1 dt

ð388Þ

Water mass for j41:

αwj IðtÞs Awj þ ht;gðj  1Þ  wj ðT gðj  1Þ T wj ÞAgðj  1Þ ¼ mwj C w

dT wj þ ht;wj  gj ðT wj  T gj Þ dx

ð389Þ

Basin liner:

αb IðtÞs ¼ hc;b  w1 ðT b  T w1 Þ þhb ðT b  T a Þ

ð390Þ

where



Q u ¼ NAC F R ðατÞC IðtÞC  U LC ðT w1  T a Þ

ð391Þ

mwj ¼ Ab dwj ρ

ð392Þ

and T wðj þ 1Þ ¼ T a

ð393Þ

It was inferred from the theoretical computations that the daily yield increases with the increase in collector area and number of collectors. It is due to the fact that there is a reutilization of latent heat of condensation more than once for higher number of effects. But the daily yield decreases with the increase of basin area and water mass in the lowest basin due to storage effect. The overall thermal efficiency increases significantly as the number of effects increases. It was suggested that the value of C and n considered by Dunkle needs modification for an active distillation system because of its higher operating temperature range. Also there is

Fig. 51. Schematics of (a) single basin double slope solar still (b) double basin double slope solar still [57].

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C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

a fair agreement between the theoretical and experimental results for single effect active distillation system. Madhlopa and Johnstone [62] presented a thermal modeling for a multi effect passive solar still with separate condenser. The system consists one basin in the evaporation chamber and two basins in the condensing chamber with a glass cover over the evaporator basin and an opaque condensing cover over third basin. The schematics of the experimental setup and the distribution of solar radiation inside the solar still are shown in Fig. 57. The water–vapor from the evaporation basin rises up and condenses on the inner side of the glass while part of the vapor flows into the condensing chamber by purging and diffusion where it condenses on the outer surface of the middle basin liner, thereby recovering part of the heat from the first effect. There is a condensing cover directly above the upper basin, with an inclined air channel (with a single open end) over the cover for cooling. The condensing cover is shielded from solar radiation by an opaque insulation cover, which forms part of the air channel. Distillate is collected by drainage channels on the bottom lower parts of the glass cover, second basin liner, third basin liner and condensing cover. The heat balance equations of the system are given as follows: Glass cover (g): dT g ¼ Ag αg IðtÞ þ Aw1 ht;w1  g ðT w1  T g Þ  Ag hc;g  a ðT g  T a Þ dt  Ag hr;g  sky ðT g  T sky Þ ð394Þ

mg C g

Basin liner 1 (b1): mb1 C b1



dT b1 ¼ Aw1 αb1 IðtÞ  hc;b1  w1 ðT b1  T w1 Þ  U b ðT b1  T a Þ dt ð395Þ

Water mass in basin 1 (w1):

dT w1 ¼ Aw1 αw1 IðtÞ þhc;b1  w1 ðT b1  T w1 Þ dt _ d hfg  Aw1 ht;w1  c ðT w1  T g Þ  Ass U ss ðT w1  T a Þ m

mw1 C w1

ð396Þ

Basin liner 2 (b2): mb2 C b2

dT b2 _ d hfgw1  Ab2 hc;b2  w2 ðT b2  T w2 Þ ¼ Aw1 hpu ðT w1  T g Þ þ m dt ð397Þ

Water mass in basin 2 (w2): mw2 C w2

dT w2 ¼ Ab2 hc;b2  w2 ðT b2  T w2 Þ dt  Aw2 ht;w2  b3 ðT w2  T b3 Þ  Ass2 U ss ðT w2  T a Þ

ð398Þ

Basin liner 3 (b3): mb3 C b3

dT b3 ¼ Aw2 ht;w2  b3 ðT w2  T b3 Þ  Ab3 hc;b3  w3 ðT b3  T w3 Þ dt ð399Þ

Water mass in basin 3 (w3): mw3 C w3

dT w3 ¼ Ab3 hc;b3  w3 ðT b3  T w3 Þ  Aw3 ht;w3  co ðT w3  T co Þ dt ð400Þ  Ass3 U ss ðT w3 T a Þ

It was observed that the productivity of the solar still with separate condenser is most sensitive to the absorptance of the evaporator basin liner, and mass of water in basins 1 and 2. Wind speed and the mass of water in basin 3 have marginal effect on distillate production. Purging is the most significant mode of vapor transfer from the evaporator into the condenser chamber, while the first effect contributes the highest proportion to the total distillate yield. It was found that the distillate productivity of the present still is 62% higher than that of the conventional type. Also the first, second and third effects contribute 60%, 22% and 18% of the total distillate yield, respectively. 7.3.5. Multistage solar still Adhikari et al. [63] examined the validity of the various correlations proposed earlier for evaluating the heat and mass transfer in a solar still by conducting steady state experiments on a two stage solar still. A simulation experiment was performed to evaluate the amount of water evaporated as a function of evaporation and condensation surface temperatures in a controlled environment. The schematic configuration of the experimental unit is shown in Fig. 58. It consists of two aluminium metallic trays kept one upon another. The upper tray is filled with water and is left exposed to the inside conditions of the room where the experiment was carried out. A hot plate type electric heater was used for indirect water heating in the lower tray. The condensate is

Fig. 52. Configuration diagram of single basin two-effect solar still [58].

Fig. 53. Energy balances in single basin two-effect solar still [58].

Fig. 54. Cross sectional view of double effect active distillation system [59].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

collected through a trough fixed at the central portion of the upper tray. The amount of distillate output collected in a time interval “t” is given by Z t he;w  g ðP w  P g Þ mew ¼ dt ð401Þ hfg 0 From the simulation results, it was observed that the following values of C and n are best suited to predict the mass transfer rate: C ¼ 0:21; C ¼ 0:1255;

n ¼ 1=4 n ¼ 1=3

for for

104 o Gr o2:51  105 2:51  105 o Gr o 107

The following relation was derived to estimate the hourly distillate yield directly: mew ¼ αðΔT 0 Þn ðP w  P g Þ

ð402Þ

where

ΔT 0 ¼ ðT w T g Þ þ

ðP w  P g ÞðT w þ 273:15Þ 268:9  103  P w

ð403Þ

The value of α is a constant for a particular operating range of a solar still. If the operating temperature range is changed, then a different value of α is required for the estimation of hourly yield. Jubran et al. [64] developed a mathematical model to predict the productivity and thermal characteristics of a multistage solar still with an expansion nozzle and heat recovery in each stage of the still. The schematic of the modified multistage solar still is shown in Fig. 59. The solar still consists of three stages placed on top of each other. There is perfect sealing between the different stages such that the water vapor which evaporated during the boiling can pass only through the small orifice that connects two stages. Vapor generated in the first stage condenses on the inclined bottom of second stage and inside the orifice passing through it, giving its heat to the water in the next stage. The rest of the vapor expands through the orifice to join the vapor generated in second stage. This expansion accelerates the rate of evaporation. The same thing happens again between second and third stages and the condenser. The heat balance equations for each stage are given as follows: Q H þðM  m3  m2 ÞC w T 2 ¼ m1 hf g1 þ ðM m1  M 2  M 3 ÞC w T 1 ð404Þ

n

897 n

MT 0 C w þ m2 hfg2 ¼ ðM  m3 ÞC w T 3 þ m3 hfg3

ð406Þ

The overall heat balance equation is given by n

Q H þ MC w T 0 ¼ ðM  m1  m2  m3 ÞC w T 1 þm1 C w T 2 þ m3 C w T 3 þ m3 hfg3

ð407Þ n

hfg ¼ hfg þ 0:68C w ðT sat  T s Þ

ð408Þ

where M, m1, m2, m3, QH, hfg, h*fg are the saline water mass flow rate, the rate of water evaporation from stage 1, the rate of water evaporation from stage 2, the rate of water evaporation from stage 3, the net solar energy transferred to the water in stage 1, the latent heat of vaporization of water and the corrected latent heat of vaporization of water at the condensation surface temperature. A computer program was developed based on the above equations and solved using the Gauss–Jordan method. It was observed that when the number of stages is increased, the yield output per added stage is decreased. At the lower values of the heat input to the still, the reduction of the water yield between one stage and another is almost negligible and becomes more significant as the heat input is increased. Also increasing the flow rate of the saline water to the solar still tends to reduce both the efficiency and the daily productivity of the solar still. But increasing the area tends to increase both the daily productivity and the efficiency. It was concluded that the daily solar still productivity can be up to 9 kg/m2, and the distillation efficiency is 87%. Hongfei et al. [65] developed a group of improved heat and mass transfer correlations to express the evaporation rate more accurately in the solar stills. For that, a multi-stage stacked tray solar still was constructed, and steady state simulating experiments were performed indoors so as to validate the correlation group. The schematic of multi-stage stacked tray distillatory with common electrical heater as heat source is shown in Fig. 60. Each tray was thermally isolated with a foamed polystyrene plank around its internal walls. The operational temperature and distillate yield in each tray were measured under steady state conditions. The experimental results were also compared with the calculated from Adhikari and Dunkle correlations. The evaporation rate per unit area of evaporation surface of the solar still is given by   hc;w  g M w P w P g mew ¼  ð409Þ ρf C f Leð1  nÞ Rgc T w T g where

n

ðM m3 ÞC w T 3 þ m1 hfg1 ¼ ðM m3  m2 ÞC w T 2 þ m2 hfg2

ð405Þ

Fig. 55. Schematic of water flowing over the glass cover of active solar still coupled with flat plate collector [60].

hc;w  g ¼ 0:2Ra0:26

Kf df

ð410Þ

In the above expression, Rgc is the universal gas constant and the value of n is taken as 0.26. The experimental hourly distillate yield for the still with single, two, and three stacked trays were compared with the calculated results. In the developed model, due to hc,w g being proportional to Ra0.26, the characteristic size (df) of the still is included, which overcomes the shortcomings of Dunkle’s correlation group not including df in the convection heat transfer coefficient. By comparing with the experimental results, it was found that the developed correlation group can be used at a wider range of temperature (35oTw o86 1C) and Rayleigh number (3.5  103 oRao2.26  107) and therefore, it is more convenient in practical applications. The theoretical yield agrees well with the experimental yield for each tray in every experiment and the mean difference is only 8.5%. Adhikari et al. [66] presented a computer simulation model to study the steady state performance of a multi stage stacked tray solar still. The model was validated by the results of simulated experiments on a three stage unit having an industrial type immersion electric heater as the heating source. The schematic

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C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

Fig. 56. Schematic of multi effect active solar still coupled with flat plate collector panel [61].

configuration of a multi stage stacked tray solar still is shown in Fig. 61. The evaporation and condensation processes occur in the distillation unit and an additional heat source in the form of a solar collector supplied heat to the distillation chamber. The metallic trays were stacked one upon another to constitute the distillation chamber. Feed water was filled in various trays through the top tray. The water in the first tray was heated by the solar collector. This caused the evaporation in the first tray and the water vapor condensed over the underside of the next tray. The latent heat released during this process was utilized for heating the water in the second tray. Subsequently, evaporation occurred in the second tray and the process continued until the last tray, which was exposed to the atmosphere. Fig. 62 shows the energy balance diagram for the modified multi stage stacked solar still coupled with the solar collector. The energy balance equations for various components of the system are given as follows: Bottom tray (Tray 1): 0 ðQ_ p;1 þ Q_ p;1 Þ  Q_ s;1  Q_ b ¼ 0

ð411Þ

Intermediate (ith) trays: 0 Q_ t;i  1  Q_ p;i þ Q_ p;i  Q_ s;i  Q_ b ¼ 0;

i ¼ 2; N þ 1

ð412Þ

Water mass in the bottom tray: 0 Q_ þ Q_ p;1 þ Q_ p;1  Q_ t;1 ¼ 0

ð413Þ

Water mass in the intermediate (ith) trays: 0 Q_ p;i þ Q_ p;i  Q_ t;i  Q_ d;i  1 ¼ 0;

i ¼ 2; N

ð414Þ

Water mass in the top (N þ 1)th tray: 0 Q_ p;N þ 1 þ Q_ p;N þ 1  Q_ t;N þ 1 ¼ 0

ð415Þ

Fig. 57. Schematics of (a) experimental setup (b) distribution of solar radiation inside the solar still [62].

The evaporative heat transfer coefficient: he;i ¼ 16:273  10  3 hc;i

ð419Þ

The distillate yield from ith stage: mew;i ¼ he;i ðT i  T p;i ÞAb;i =hfg;i ;

i ¼ 1; N

ð420Þ

where “p” refers to the tray, “s” denotes the side walls and “N” represents the number of stages. Also, Q and Q0 represent the amount of energy transferred from horizontal and vertical portions to water, respectively. A computer programme was developed to predict the steady state water temperature of different stages and to the corresponding distillate yield from each stage. It was observed that the daily distillate yield increases with a corresponding increase in the number of stages of the distillation system. However, the fractional increase in daily distillate yield decreases with the introduction of any new stage. The theoretical values were in reasonably good agreement with the experimental results. 7.3.6. Tilted wick solar still Tanaka and Nakatake [67] presented a numerical analysis to investigate the effect of a vertical flat plate external reflector on the distillate productivity of the tilted wick solar still. Fig. 63 shows the schematic of the tilted wick solar still with vertical flat plate external reflector. The still consists of a glass cover, evaporating wick and a vertical flat plate external reflector of highly reflective materials such as a mirror finished metal plate. Saline water is fed to the wick constantly. The direct and diffuse solar radiation and also the reflected solar radiation from external reflector are transmitted through the glass cover and absorbed onto the wick. The energy balance for the glass cover and the evaporating wick are expressed as follows:

The convective heat transfer coefficient: hc;i ¼ CðGr i Pr i Þn K i =xi Gr i ¼

ð416Þ ð417Þ

μ2i

ΔT 0i ¼ ðT i  T p;i þ 1 Þ þ

dT g dt ð421Þ

ðdf Þ3i ρ2i β g ΔT 0i "

Q sun;g þ Q r;w  g þ Q d;w  g þ Q e;w  g ¼ Q r;g  a þ Q c;g  a þ ðMCÞg

ðP e;i  P c;i ÞðT i þ 273:15Þ 268:9  103  P e;i

# ð418Þ

Q sun;w ¼ Q r;w  g þ Q d;w  g þ Q e;w  g þQ d;w  a þ Q f þ ðMCÞw

dT w dt

ð422Þ

where Qsun,g and Qsun,w are the solar radiation absorbed on the glass cover and the evaporating wick, and Qr, Qcd, Qc and Qe are the heat transfer rates by radiation, conduction, convection, and

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

evaporation and condensation. Qf is the increase in the enthalpy of the saline water fed to the wick. The solar radiation absorbed on the glass cover and the evaporating wick can be determined as follows: For a still with an external reflector: i αg h ð423Þ Q sun;g ¼ ðQ sun;dr þ Q sun;re Þ=τg ðβ g Þ þQ sun;df =ðτg Þdf

αw

Q sun;w ¼ Q sun;dr þ Q sun;re þQ sun;df The value of

ð424Þ

τg ðβg Þ ¼ 2:642 cos βg  2:163 cos 2 βg 0:320 cos 3 βg þ 0:719 cos 4 βg ð425Þ

ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g  T a Þ

ð428Þ

Energy balance for the water mass, considering a small elemental length “dx” of constant width “b” is given by   0

dT w _ w Cw dx αw IðtÞs  ht;w  g ðT w T g Þ  hb ðT w T a Þ bdx ¼ m dt The average value of water temperature can be found as

Tw ¼

α0w UL

 IðtÞs þ T a

1

   _ wCw _ w Cw expð  As U L =m expð  As U L =m þTw 1 _ _ A s U L = mw C w As U L =mw C w

ð430Þ

For a still without the external reflector: i αg h Q sun;dr =τg ðβg Þ þ Q sun;df =ðτg Þdf Q sun;g ¼

ð426Þ

Q sun;w ¼ Q sun;dr þ Q sun;df

ð427Þ

In the above expressions, Qsun,dr, Qsun,re, and Qsun,df are the direct solar radiation absorbed on the evaporating wick, the solar radiation reflected from the external reflector and absorbed on the wick, and the diffuse solar radiation absorbed on the wick, respectively. It was observed that the average daily amount of distillate peaks when the angle of the still θ ¼201 for the still with reflector, and peaks at θ ¼301 for the still without reflector. Also the average daily amount of distillate of the still with reflector is predicted to be about 9% larger than that of the still without reflector, and the vertical flat plate external reflector would be less effective for the tilted wick still than for the basin still. 7.3.7. Multi-wick solar still Shukla and Sorayan [68] derived expressions for water and glass temperatures, yield and efficiency of both single and double slope multi wick solar distillation system in quasi-steady state conditions. Figs. 64 and 65 show the schematics of single slope and double slope multi wick solar still, respectively. In these type of solar stills, one end of a number of wet jute cloth pieces (porous fibers) of different lengths are dipped into a water reservoir while the other ends are spread over the absorber basin as shown in diagrams. The jute cloth pieces are blackened and placed one upon the other, separated by polythene sheets. Here, the wet piece of jute cloth forms the water surface in the still. It could attain a higher temperature due to its negligible heat capacity. This leads to rapid evaporation of water.

Fig. 58. Schematic configuration of experimental setup [63].

The energy balance equations for different components of the stills are given as follows: Energy balance for glass cover:

ð429Þ

τg(βg) can be calculated as follows:

αw

899

where U L ¼ U t þhb The computer programs were developed to predict the hourly water temperature, glass temperature, distillate output and various heat transfer coefficients for both the solar stills. This model takes the modified values of convective heat transfer coefficients based on both inner and outer glass temperatures, carries out the computations of all performance parameters, and then compares them with the experimental data. Values of C and n for single and double slope multi wick solar stills were evaluated based on the Kumar and Tiwari model. It was observed that the values of internal convective heat transfer coefficient between water and inner glass surface (hc,w  g) based on the inner glass cover temperature are greater than the values based on the outer glass cover temperature. It is due to fact that (Tw  Tgi) is small but has higher operating temperature. The value of internal convective heat transfer coefficients evaluated by present model is much higher than value obtained by Dunkle’s model. Also the radiative and convective heat transfer coefficients do not vary significantly for both, the inner as well as the outer glass temperatures, unlike evaporative heat transfer coefficient for single as well as double slope multi wick solar stills. But the inner glass cover temperature for single slope multi wick solar stills is higher than outer glass cover temperature. It was concluded that in winter, single slope solar still gives higher efficiency in comparison with double slope solar still due to more reflection losses from double slope solar still and this is reversed in summer. 7.3.8. Tubular solar still Ashan and Fukuhara [69] proposed a mass and heat transfer model of a Tubular Solar Still (TSS) by incorporating various mass and heat transfer coefficients taking account of the humid air

Fig. 59. Schematic of the multistage evacuated stack solar still [64].

900

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

properties inside the still. The validity of the proposed model was verified using the field experimental results. The mechanism of pure water production in tubular solar still is shown in Fig. 66. It consists of a transparent tubular cover and a blackened rectangular trough inside the cover. The solar radiant heat after transmitting the cover is mostly absorbed by the saline water in the trough and the rest is absorbed by the cover and the trough. Thus, the saline water is heated up and evaporated. The water vapor density of the humid air increases associated with the evaporation from the water surface and then the water vapor is condensed on the inner surface of the cover, releasing its latent heat due to evaporation. Finally, the condensed water naturally trickles down toward the bottom of the cover due to gravity and is stored in a collector. Fig. 67 shows the heat and mass transfer inside and outside of the tubular solar still. The energy balance equations of the proposed tubular solar still are given as follows: Water: ðρCÞw

∂ðV w T w Þ ¼ τw Aw IðtÞs þ Q t;w  Q e;w  Q c;w  Q r;w ∂t

can precisely predict the daily and hourly production of the tubular solar still. Chen et al. [70] analyzed the characteristics of heat and mass transfer of a three-effect tubular solar still. Fig. 68 shows the operating mechanism and energy transfer in a three effect tubular solar still. In this still, solar energy or industrial residual heat is utilized as the heat source. The external energy can heat the seawater in first effect water trough through heat exchanger tube and convert it into the freshwater vapor which may condense into fresh water due to the low temperature seawater in second effect water trough, and finally the fresh water may flow along the tube wall to the bottom. The evaporation latent heat released during the process of condensation may heat the seawater in the second effect water trough and the energy can be transferred from the first effect to the second effect in a convective and radiative way, thus heating the seawater at the second effect. The whole process will repeat till the freshwater vapor at the last and third effect is

ð431Þ

Humid air: ðρCVÞha

∂T ha ¼ τha Aha IðtÞs þ Q e;w þ Q c;w þ Q t;ha  Q c;ha  Q cd;ha ∂t

ð432Þ

Cover: ðρCVÞc

∂T c ¼ τc Dtss Lc IðtÞs þ Q c;ha þ Q cd;ha þ Q r;w  Q c;c  Q r;c ∂t

ð433Þ

Trough: ðρCVÞt

∂T t ¼ τt1 Aw IðtÞs þ τt2 IðtÞs ðBt Lt  Aw Þ  Q t;w  Q t;ha ∂t

ð434Þ

In the above expressions, “ha”, “c” and “t” represent humid air, cover and trough, respectively. Also “Bt” and “Dtss” denote the width of the trough and diameter of the tubular solar still, respectively. Computer simulation was carried out to calculate various parameters involved in the desalination process. The proposed model was made possible to provide some new outputs for the TSS such as the temperature, water vapor density and relative humidity of the humid air, and the condensation flux besides the temperatures of the water, cover and trough, and the hourly evaporation flux. It was observed that the difference between the evaporation and condensation rates strongly affects the diurnal variation of the water vapor density in the humid air and the relative humidity. Also the calculated profiles were compared with the field experimental results and proved that the proposed model was capable to reproduce the observed temperatures of the water, trough, humid air and cover, relative humidity of the humid air and the water vapor density in the humid air. The proposed model

Fig. 60. Schematic configuration of a multi stage staked tray solar still [65].

Fig. 61. Schematic configuration of a multi stage stacked tray solar still [66].

Fig. 62. Energy balance diagram for a multi stage stacked tray solar still [66].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

condensed on the tube pipe with the heat radiating into the surrounding air. The fresh water produced at three effects will flow into a storage tank. The energy equilibrium in the three effects tubular solar still is given as follows: First effect energy equilibrium: Q i ¼ Q 1r þ Q 1e þ Q 1c þ ðρCVÞ1

dT 1 dt

ð435Þ

Second effect energy equilibrium: Q 1r þ Q 1e þ Q 1c ¼ Q 2r þ Q 2e þ Q 2c þ ðρCVÞ2

dT 2 dt

ð436Þ

dT 3 dt

ð437Þ

Third effect energy equilibrium: Q 2r þ Q 2e þ Q 2c ¼ Q 3r þ Q 3e þ Q 3c þ ðρCVÞ3

Energy equilibrium between apparatus and environment: Q 3r þ Q 3e þ Q 3c ¼ Q rc þ Q cc þ ðρCVÞc

dT a dt

ð438Þ

In the above expressions, the temperature of condensation tube at each effect is equal to that of water trough at next effect and “Qi” is the energy input of apparatus. The fixed temperature experiments at normal pressure and negative pressure indicate that the desalination water yield rate rises in a steady condition as the temperature increases and the vacuum degree goes up, increasing much faster especially during the phase of high temperature. When the pressure inside the still reduces to the saturation vapor pressure of the first level water temperature, the desalination water yield at a steady condition is several times as much as that at normal pressure, which increases by 467%, 342% and 317% when the temperature keep at 60 1C, 70 1C and 80 1C, respectively. It was concluded that the optimal combination of all parameters such as temperature, pressure, power and relevant dimensions, is an effective way of improving the energy use efficiency as well as the desalination water yield. 7.3.9. Inverted absorber solar still Tiwari and Suneja [71] derived analytical expressions for water temperature, condensing cover temperature, hourly yield and instantaneous thermal efficiency of an inverted absorber solar still. The water temperature in the distillation system was increased by inverting the absorber to reduce the bottom heat loss. The solar radiation, after transmission through the glass cover 1, was reflected back to the inverted absorber of the solar still as shown in Fig. 69. The absorbed solar radiation was partially transferred to the water mass above the inverted absorber by convection while rest of the radiation was lost to the atmosphere through the glass covers g1 and g2. The evaporated water was condensed on the inner surface of the condensing cover, releasing its latent heat. The energy balance equations for inverted absorber solar still are given as follows: Absorber plate (pl):

τg1 τg αpl Rnr IðtÞ ¼ hc;pl  w ðT pl T w Þ þ hr;pl  g ðT pl  T g Þ

901

It was observed that there is a significant increase in the water temperature of the inverted absorber solar still due to reduced bottom heat loss and higher absorptivity of the absorber plate. Also the inverted absorber solar still gives about double the output of the conventional solar still. The radiative and convective heat transfer coefficients of the inverted absorber solar still do not vary much with the change in water depth. However, the evaporative heat transfer coefficient significantly depends on water depth due to the increase in water temperature as the depth decreases. Suneja and Tiwari [72] presented a transient analysis of an inverted absorber double basin solar still shown in Fig. 70 and derived the expressions for the water temperatures of various components and the efficiency. The effect of water depth in the lower basin of the still, keeping the depth in the upper basin constant, on the water and condensing cover temperatures, the heat transfer coefficients and the yield were also investigated. The energy balance equations for inverted absorber double basin solar still are given as follows: Glass plate (g): hr;pl  g ðT pl  T g Þ ¼ U bk ðT g  T a Þ

ð443Þ

Absorber plate (pl):

τg1 τg αpl Rnr IðtÞ ¼ hc;pl  w1 ðT pl  T w1 Þ þ hr;pl  g ðT pl  T g Þ

ð444Þ

Water mass (w1): hc;pl  w1 ðT pl  T w1 Þ ¼ ðm1 CÞw

dT w1 þ ht;w1  g1 ðT w1  T g1 Þ dt

ð445Þ

Condensing cover (g1): ht;w1  g1 ðT w1  T g1 Þ ¼ hc;g1  w2 ðT g1  T w2 Þ

ð446Þ

Water mass (w2): hc;g1  w2 ðT g1  T w2 Þ ¼ ðm2 CÞw

dT w2 þ ht;w2  g2 ðT w2  T g2 Þ dt

ð447Þ

Condensing cover (g2): ht;w2  g2 ðT w2  T g2 Þ ¼ hc;g2  a ðT g2 T a Þ

ð448Þ

Based on the numerical calculations, it was observed that the depth of water in the lower basin of the still is a significant parameter and that the water and condensing cover temperatures and the yield decrease as the depth of water in the lower basin

ð439Þ

Water mass (w): hc;pl  w ðT pl  T w Þ ¼ mw C w

dT w þ qr;w  g1 þ qe;w  g1 þ qc;w  g1 dt

ð440Þ

Condensing cover (g1): qr;w  g1 þ qe;w  g1 þ qc;w  g1 ¼ qr;g1  a þ qc;g1  a

ð441Þ

Glass plate (g): hr;pl  g ðT pl  T g Þ ¼ U b ðT g  T a Þ

ð442Þ

Fig. 63. Schematic of tilted wick solar still with vertical flat plate external reflector [67].

902

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

increases. It was also inferred that the total yield from the system is maximum for the least water depth in the lower basin. Suneja and Tiwari [73] presented a computer simulation model based on first order Runge–Kutta fourth order method for a multi basin inverted absorber distiller unit. The results obtained from simulation were compared with single and multi basin inverted absorber solar stills. Fig. 71 shows the schematic of inverted absorber seven basins solar still. In a conventional solar still, the same glass surface is used for input as well as output of energy, whereas in an inverted absorber solar still, two different surfaces are used—the absorber plate at the bottom for the input and the corresponding cover at the top for output energy. The energy balance equations for inverted absorber solar still are given as follows: Glass plate (g): hr;pl  g ðT pl  T g Þ ¼ U bk ðT g  T a Þ

ð449Þ

Absorber plate (pl):

τg1 τg αpl Rnr IðtÞ ¼ hc;pl  w1 ðT pl  T w1 Þ þ hr;pl  g ðT pl  T g Þ

ð450Þ

Water mass (w1): hc;pl  w1 ðT pl  T w1 Þ ¼ ðm1 CÞw

dT w1 þ ht;w1  g1 ðT w1  T g1 Þ dt

ð451Þ

Condensing cover (g1): ht;w1  g1 ðT w1  T g1 Þ ¼ hc;g1  w2 ðT g1  T w2 Þ

ð452Þ

The energy balance on water mass and condensing cover can be written in general form as follows: Water mass: hc;gm  wðm þ 1Þ ðT cm  T wðm þ 1Þ Þ dT wðm þ 1Þ þ ht;wðm þ 1Þ  gðm þ 1Þ ðT wðm þ 1Þ  T gðm þ 1Þ Þ ¼ ðmm þ 1 CÞw dt ð453Þ

¼ hc;gðm þ 1Þ  wðm þ 2Þ ðT gðm þ 1Þ T wðm þ 2Þ Þ

where m ri  2 For m ¼i  1, the energy balance on condensing cover is modified as follows: ht;wðm þ 1Þ  gðm þ 1Þ ðT wðm þ 1Þ  T gðm þ 1Þ Þ ¼ hc;gðm þ 1Þ  a ðT gðm þ 1Þ  T a Þ ð455Þ It was observed that water and condensing cover temperatures decrease if the number of effect is increased due to the fact that available energy for a given basin is lower than the preceding basin. The yield increases as the number of effects in the multi effect inverted absorber solar still is increased and reaches an optimum value when the number of basin is seven. But, for eight and nine basin solar stills, there is only a marginal increase in the yield. Thus it is concluded that seven is the optimum number of basins in a multi-effected inverter absorber solar still. The yield from a seven effect inverted absorber solar still is about 4.2 times that from an inverted absorber single basin solar still. Also the total yield decreases with an increase in the depth of water in the lowest basin for each of the multi effect inverted absorber solar still. Yadav and Yadav [74] conducted a transient analysis on a basin type solar still integrated with an inverted absorber asymmetric line-axis solar compound parabolic concentrator. Mathematical expressions were obtained for water temperature, glass cover temperature, water–glass cover temperature difference, distillate output and efficiency of the system. The schematic of the proposed system is shown in Fig. 72. The energy balance equations at various components of the proposed system can be written as follows: Absorber/basin liner: ð1  αg Þð1 þ C r Rnr Þαb Ab IðtÞs ¼ Ab hw ðT b  T w Þ þAb hb ðT b  T a Þ

Condensing cover:

ð454Þ

ð456Þ

ht;wðm þ 1Þ  gðm þ 1Þ ðT wðm þ 1Þ  T gðm þ 1Þ Þ

Fig. 64. Schematic of single slope multi wick solar still [68].

Fig. 66. Mechanism of pure water production in tubular solar still [69].

Fig. 65. Schematic of double slope multi wick solar still [68].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

903

distilled water is found less than 7 i.e. acidic in nature and low electrical conductance is due to low values of the TDS in the distilled water obtained from the inverted absorber solar still and the single slope solar still. The theoretical results were in fair agreement with the experimental results for the inverted absorber solar still at water depths 0.01, 0.02 and 0.03 m only for the daytime operation.

7.3.10. Pyramid shaped solar still Hamdan et al. [76] performed theoretical as well as experimental analysis to find the performance of the pyramid shaped single, double and triple basin solar stills. Fig. 73 shows the cross sectional view of the pyramid shaped cover triple basin solar still. The energy balance equations of the solar still are given below: Basin water:

αw τIðtÞ ¼ qb þ C w ðdT w =dtÞ þqe;w  g þ qr;w  g þ qc;w  g

ð462Þ

Glass cover: qe;w  g þ qr;w  g þqc;w  g þ αg IðtÞ ¼ qt;g  a þ C g ðdT g =dtÞ Fig. 67. Heat and mass transfer inside and outside of the tubular solar still [69].

Ab hw ðT b  T w Þ ¼ mw C w

Basin and cover assembly:

αg IðtÞ þ αw τIðtÞ ¼ qt;g  a þ qb þ C w ðdT w =dtÞ þC g ðdT g =dtÞ

Water in the basin: dT w þ Ab ht;w  g ðT b  T g Þ dt

ð457Þ

Glass cover: Ab ht;w  g ðT w  T g Þ ¼ Ab ht;g  a ðT g  T a Þ

ð458Þ

Based on the numerical calculations, it was observed that water temperature, glass cover temperature, temperature differential across water-to-glass cover, distillate output and instantaneous efficiency of the system decrease with increasing water mass in the basin. These parameters increase with increasing absorptivity of the basin liner and the concentration ratio. Hence it was concluded that the water mass, absorptivity and concentration ratio have a profound effect on the distillate output and overall efficiency of the system. Dev et al. [75] investigated the performance of inverted absorber solar still and single slope solar still at different water depth and total dissolved solid and compared the observed results. Also the thermal model for inverted absorber solar still was developed and validated by experimental results. The energy balance equations for basin, water, and condensing glass cover of the inverted absorber solar still are given below: Absorber basin plate:

α″b Ab IðtÞs ¼ hw Ab ðT b  T w Þ þH 2 Ab ðT b  T a Þ

ð463Þ

ð464Þ

From the study, it was observed that the triple basin still has a maximum daily efficiency of 44%, and those of the double and single basin stills are 42% and 32%, respectively. Also there is a fair agreement between the obtained values of the efficiencies and the predicted ones. It was concluded that the triple solar still is of maximum daily efficiency followed by the double still, with the single still of the least efficiency.

7.3.11. Triangular solar still Rubio-Cerda et al. [77] investigated the performance of the condensing cover of an attic shaped solar still under two orientations, east–west and north–south. A procedure was proposed as an extension to Dunkle’s model to estimate the contribution from each condenser to the total mass flow rate in stills with triangular geometry. Fig. 74 shows the main characteristics of the experimental still.

ð459Þ

Water mass:

α0w Ab IðtÞs þ hw Ab ðT b  T w Þ ¼ ðMCÞw

dT w þ ht;w  gi Ab ðT w T gi Þ þ H 3 Asw ðT w  T a Þ dt

ð460Þ

Condensing glass cover (g)

α

0 g Ag IðtÞs þ ht;w  gi Ab ðT w T gi Þ ¼

H 1 Ag ðT gi T a Þ

ð461Þ

where H1, H2, and H3 are the total heat transfer coefficient between glass cover–ambient, basin plate–ambient, and water mass–ambient systems, respectively. From the analysis, it was observed that as the water depth increases the yield of both type solar still decreases. The maximum optimized water depth can be taken as 0.03 m for the inverted absorber solar still at which the addition of reflector under the basin does not affect its performance considerably in comparison to that of the single slope solar still. The values of pH for the

Fig. 68. Schematic of energy transfer in a three-effect tubular solar still [70].

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The partial pressures used in Dunkle’s relations are calculated as follows: P ¼ 22125883:19  10  Xða þ bX þ cX

3

Þ=½Tð1 þ dXÞ

ð465Þ

where X ¼ 647:27–T

a ¼ 3:2437814

c ¼ 1:1702379  10  8

b ¼ 5:86826  10  3

d ¼ 2:1878462  10  3

Then, a procedure that considers the superposition of the effects of temperature differences and fractional area is proposed. In a first step, the production rate for each cover with the corresponding temperature differences and partial water vapor– air pressures by means of Dunkle’s relations, as if they were two separate stills, is estimated. Then, the production of each cover is modified by the corresponding fraction of cover area. In mathematical terms, mn1 ¼ mðT w ; T 1 ; P w ; P 1 Þ

ð466Þ

mn2 ¼ mðT w ; T 2 ; P w ; P 2 Þ

ð467Þ

m1 ¼ f 1 mn1

ð468Þ

n

ð469Þ

m2 ¼ f 2 m2 where f1 ¼

L1 L1 þ L2

ð470Þ

f2 ¼

L2 L1 þ L2

ð471Þ

In the above expressions, L1 and L2 are the perimeter lengths of first and second condensing covers, respectively, and m* denotes the modified mass transfer rate. From the numerical predictions, larger differences in the condensers’ temperatures and distillate performance were found for the still with covers facing east–west, due to the conditions of solar radiation incidence. For short time periods during sunrise, when covers may be hotter than water, the distillation process stops completely. The proposed model extension reproduces satisfactorily the measured production of each cover in a still with symmetric double slope and the results are expected to be valid for Grashof numbers up to 1.7  108. 7.3.12. Stepped solar still Velmurugan et al. [78] conducted analysis on a stepped solar still to improve its productivity by maintaining minimum water depths in the basin. The productivity by the usage of trays with two different water depths, integrating fins at the basin, and usage

Fig. 69. Schematic of inverted absorber solar still [71].

of sponges in stepped solar still were also investigated. Theoretical analysis was made by solving energy balance equations and compared with experimental results. The schematic of the stepped solar still is shown in Fig. 75. The absorber plate in the solar still is like a stepped structure and there are totally 50 trays in the absorber plate. Fig. 76 shows the energy analysis in the stepped solar still. The energy balance equations are as follows: Absorber plate: IðtÞs Ab αb ¼ M b C b

dT b þ Q w þ Q loss dt

ð472Þ

Water mass: IðtÞs Aw αw þ Q w ¼ Q c;w  g þ Q r;w  g þ Q e;w  g þM w C w

dT w dt

ð473Þ

Glass cover: dT g dt ð474Þ

IðtÞs Ag αg þ Q c;w  g þ Q r;w  g þ Q e;w  g ¼ Q r;g  sky þQ c;g  sky þ M g C g

From the analysis, it was found that the production rate of water increases 80% when fin and sponge type stepped solar still is used in comparison with ordinary stepped solar still. The integration of fin in the basin plate gives more evaporation rate than adding sponges and maximum productivity occurs when both are combined. Also the experimental results showed that the productivity increased by 76%, 60.3% and 96% when fins, sponges and combination of both fins and sponges were used, respectively. The theoretical analysis gave good agreement between experimental results and the maximum deviation was found to be less than 10%. Velmurugan et al. [79] conducted an experimental investigation to desalinate industrial effluent with the help of a stepped solar still shown in Fig. 77 and made theoretical analyses by solving energy balance equations. The concept of integrating the fin at the basin solar air heater was also introduced in the stepped solar still. The industrial effluent was used as raw water in the still. Pebbles and sponges were also used in the basin to enhance the productivity. The energy balance equations for absorber plate, water mass and glass cover are same as mentioned in Velmurugan [78]. It was found from the experimental investigation that the production rate increased by 53.3% when fins were used in the stepped solar still. When sponge and pebble were used, the productivity increased by 68% and 65%, respectively. Also, using both sponge

Fig. 70. Schematic of an inverted absorber double basin solar still [72].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

and pebble in fin type stepped solar still increased the productivity by 98% than the conventional stepped solar still. The theoretical predictions closely agree with experiment result and the maximum deviation between theoretical and experimental analyses is less than 10%. Kabeel et al. [80] carried out both experimental and theoretical investigation on a stepped basin solar still. The influence of depth and width of trays on the performance of the still was investigated. The absorber plate of the still was made of five steps and a wick on the vertical sides was added to improve its productivity. The feed water was preheated by an evacuated tubes solar collector and the effect of feed water temperature in the stepped still was also investigated. The schematic of the stepped solar still with the solar collector is shown in Fig. 78. The energy balance equations are as follows: Basin plate: IðtÞs Ab αb ¼ M b C b

dT b þQ w þQ loss dt

ð475Þ

Saline water: IðtÞs Aw αw þQ w ¼ M w C w

dT w þQ c;w  g þ Q r;w  g þ Q e;w  g þ Q f w dt ð476Þ

Glass cover: IðtÞs Ag αg þ Q c;w  g þ Q r;w  g þ Q e;w  g ¼ M g C g

dT g þ Q r;g  sky þQ c;g  sky dt ð477Þ

where, Qfw is the heat taken by the flowing water and is calculated as Q f w ¼ mf w C f w ðT a  T w Þ

ð478Þ

From the experimental and theoretical results, it was observed that the productivity of the stepped still decreases by increasing the water depth. The higher performance of stepped still is achieved at water depth of 5 mm and tray width 120 mm which is 57.3% higher than the productivity of the conventional still. Also using the wick on the vertical sides of the stepped still increases

905

the daily productivity by 3–5%. It was inferred that preheating the feed water of the stepped still has a slight effect on the enhancement of the productivity, but the efficiency of the system decreases approximately to the half. It was concluded that there is a good agreement between the theoretical results and the experimental data. The deviations between experimental and theoretical results for conventional still are ranging from 5% to 8%. But for stepped still the deviations are ranging from 7% to 13%. 7.3.13. Weir type solar still Sadineni et al. [81] developed mathematical models to predict the hourly distillate productivity of a weir type solar still. The still was used to recover the rejected water from the water purifying system for solar hydrogen production. The schematic of the proposed system is shown in Fig. 79. It is an inclined type still, which consists of a weir-shaped absorber plate, cover/condensing glass, distillate collection trough, water circulation system and support structure. The weirs help to distribute the water evenly and increase the time spent on the absorber surface. Both singlepane and double-pane tempered glass covers were used as condensing surfaces. The productivity of the weir-type still with a single-pane glass was also compared with conventional basin type solar still. Water flows from the top basin, over the weirs and finally, to the bottom basin and small pump is used to return the unevaporated water to the top basin. The flow rate of circulating water is controlled by a valve in the system. The water temperature for a single-pane glass cover still is given as

     τw U LS bdx U LS bdx Tw ¼ 1  exp  þT w0 exp  IðtÞs þ T a _ wCw _ w Cw m m U LS ð479Þ The energy balance equations for double-pane glass cover still are given as follows: Inner glass: ht;w  gi ðT w  T gi Þ ¼ ht;gi  go ðT gi  T go Þ

ð480Þ

Outer glass: ht;gi  go ðT gi T go Þ ¼ ht;go  a ðT go  T a Þ

ð481Þ

Flowing water:



_ w Cw τw IðtÞ  ht;w  gi ðT w  T gi Þ  hb ðT w  T a Þ bdx ¼ m

  dT w dx dt ð482Þ

It was found that there is a significant reduction in the performance with a double-pane glass compared with a singlepane glass. Due to the reduced temperature difference between the evaporating water and condensing glass in a still with doublepane glass used both as transparent cover and condensing surface,

Fig. 71. Schematic of an inverted absorber seven basin solar still [73].

Fig. 72. Schematic of an inverted absorber asymmetric line-axis solar compound parabolic concentrating solar energy collector [74].

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C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

the productivity reduced significantly. It was also observed that the proposed design improved the productivity about 20% compared with a conventional basin-type solar still. Scale formation on the absorber surface in the case of an inclined still with conventional wicks is also avoided by using the weir-type design and a small recirculation pump. Tabrizi et al. [82] studied the influence of water flow rate on the internal heat and mass transfer and daily productivity of a cascade solar still. The well-known Dunkle’s relation was employed to predict the still behavior. Fig. 80 shows the schematic diagram of the proposed cascade solar still. The still was designed to increase the amount of distillated water production by providing a minimum air gap, suitable distribution of feed water on evaporation surface and better orientation to solar beams. Each step inside the still was equipped with a weir to force the flowing water to pass through the evaporation surface, which leads to the increase of the residence time of water in the still. Moreover, the weirs were to keep the water film as shallow as possible (with low heat capacity) and cause to improve the water distribution upon the evaporation surface while avoiding dry spots. Hence, the channeling was diminished by even distribution of water on the absorber plate. The values of C and n in the Nusselt’s expression were calculated from the experimental data. The average values of C and n were found to be 1.22 and 0.22, respectively. It was observed that the convective heat transfer coefficient is not strongly temperature dependent in comparison with the evaporative heat transfer coefficient. It was inferred that the Dunkle’s model could not satisfy the cascade solar still behavior since the Dunkle’s convective heat is proportional to the temperature difference between water and glass cover surfaces (ΔT). In the cascade solar still, the low distance between the surface of water and glass cover result in low values of ΔT which leads to low values of heat and mass transfer coefficients using Dunkle’s relation. Also, the increase in the flow rate caused to decrease in daily productivity and overall thermal efficiency. The daily productivity was obtained about 7.4 and 4.3 kg/m2/day for minimum and maximum flow rates, respectively. The maximum and minimum overall efficiencies for minimum and maximum flow rates were also obtained about 63.3% and 36.6%, respectively. Dashtban and Tabrizi [83] analyzed a weir type cascade solar still integrated with latent heat thermal energy storage system for enhancing the productivity. A mathematical model was developed and solved based on the Dunkle’s relations. The model results were validated with experimental data produced from the designed still to show the necessity of calculation of the new convective heat transfer coefficient. Also a theoretical analysis was carried out to investigate some effective parameters on the still

productivity like water depth and air gap. Fig. 81 shows the schematic of the weir type cascade solar still with phase change material (PCM) as an energy storage medium. The usage of a heat storage system with paraffin wax (PCM) beneath the absorber plate kept the operating temperature of the still high enough to produce distillated water during the lack of sunshine, particularly at night. The energy balance equations for various elements of the still are as follows: Glass cover: IðtÞs αg þ ht;w  g ðT w  T g Þ ¼ ht;g  a ðT g T a Þ þ

M g C g dT g Ag dt

ð483Þ

M w C w dT w Aw dt

ð484Þ

Brackish water: IðtÞs τg αw þ hw ðT b  T w Þ ¼ ht;w  g ðT w  T g Þ þ Absorber plate with PCM: IðtÞs αb τg τw ¼ hw ðT b  T w Þ þ ðK pcm =Lpcm ÞðT b  T pcm Þ þ

M b C b dT b Ab dt ð485Þ

Phase change material: ðK pcm =Lpcm ÞðT b T pcm Þ ¼ ðK ins =Lins ÞðT pcm  T a Þ þ

M equ dT pcm Ab dt

ð486Þ

Absorber plate without PCM: IðtÞs αb τg τw ¼ hw ðT b  T w Þ þ U b ðT b  T a Þ þ

M b C b dT b Ab dt

ð487Þ

From the experimental and theoretical investigations, it was observed that using a weir on the edge of each step of the stills leads to even distribution of water onto the evaporation surface and increases the residence time. It is suggested that the convective heat transfer coefficient, very important parameter in the still modeling, should be determined from the produced experimental data for different still geometries and operational conditions. It was also found that increasing the level of water on the evaporation surface and decreasing the air gap in the still lead to decrease and slightly increase in the total productivity of the still, respectively. It was concluded that the still with PCM is superior in productivity compared with still without PCM by about 31%. The daily productivity was theoretically obtained about 6.7 and 5.1 kg/ m2/day for still with and without PCM, respectively. The overall thermal efficiency of the still with PCM was 64% and for still without PCM was 47%. 7.3.14. Inverted trickle solar still Badran et al. [84] presented a mathematical model to predict the performance of an inverted trickle solar still. The schematics and the cross sectional view of the still with heat exchanger is shown in Figs. 82 and 83. In this still, the saline water was allowed to flow on the back side of an absorber plate. The water was remained on the plate with the help of a porous material fixed on its back. A low water flow rate was maintained such that its temperature was raised enough to produce vapor. The condensation occurred in another compartment where condensate was collected. The concept of reduced salinity was investigated by using the brackish water feed at 6000 ppm. The energy balances on various components of the still are given as follows:Absorber plate (pl): _ g ÞC w ΔT 0sw ðατÞeff IðtÞs ¼ q0e þ qpl  g þqss þ ðm=A

ð488Þ

0

where q e the heat carried out by evaporation from absorber plate. Glass cover (g): Fig. 73. Cross sectional view of the triple basin solar still [76].

qpl  g ¼ qg  a

ð489Þ

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

907

Fig. 74. Schematic of the triangular solar still [77].

Lower condenser plate: q″e ¼ q0b

ð490Þ

where q0 b is the heat loss from lower condenser plate and q″e is the heat carried out by vapor to condenser plate. Exchanger (hx): _ g ÞC w ðT sw;ex  T sw;in Þ qhx ¼ ðm=A

ð491Þ

The energy balance on the whole still is given by _ g ÞC w ΔT 0sw ðατÞeff IðtÞs ¼ qhx þ q0b þ qg  a þ qss þ ðm=A

ð492Þ

It was observed that the productivity of the inverted trickle solar still is moderately improved by using brackish water. The productivity increased from 2.5 to 2.8 l/day when the salinity of the water was reduced from that of sea water (35,000 ppm) to brackish water (6000 ppm). But the simulation results overpredict the experimental results by about 35–40% due to the use of a clear sky model. The simulation was based on steady state performance and did not take into account the transient behavior of the still. Also decreasing the feed water flow rate increases the productivity of the still. It was suggested that a large amount of production of water of reduced salinity is possible by mixing the yield of the condensate and the intermediate headers.

7.3.15. Inclined solar still Aybar [85] presented a mathematical modeling for an inclined solar water distillation system and investigated the effects of feed water mass flow rate and solar intensity on the system parameters. Unlike solar still system, the water flows in an inclined solar distillation system. Fig. 84 shows the schematic of the proposed system. It consists mainly of an absorber plate and a glass cover which create a cavity. The absorber plate is covered by a black wick in order to distribute water on the plate evenly and to increase the thickness of the water film. The system is inclined at an angle of 301 in order to allow the dripping water to run down on the absorber plate and to insure that the solar rays are normal to the surface at most times of the day. The feed water falls onto the black absorber plate or black wick on the absorber plate creating a layer of water all over the absorber plate. Solar energy warms the absorber plate and black wick. Some of the water on the absorber plate evaporates and condenses when it touches the cool glass cover. The condensate flows into a condensate channel and is taken out of the side of the cavity. The rest of the feed hot water flows into another collection channel and the hot water is removed from the bottom center of the remaining water channel. The system was modeled using time-dependent energy balance and mass balance equations, and the equations were solved the using 4th-order Runge–Kutta method. The energy balance equations are given as follows:

Fig. 75. Schematic of stepped solar still [78].

Fig. 76. Energy analysis in stepped solar still [78].

Absorber plate: M pl C pl

dT pl ¼ IðtÞτg αpl  Q r;pl  g  Q c;pl  w dt

ð493Þ

Water film:

ρw C w bwf

dT w;ex 1 _ in T w;in  m _ ex T w;ex Þ þ Q c;pl  w  Q evap ¼ C w ðm Lc dt

ð494Þ

Glass cover: Mg C g

dT g ¼ Q r;pl  g þ Q cond  Q r;g  a  Q c;g  a dt

ð495Þ

Pv P sat

ð496Þ

Q cond ¼ 85:0ðT mix  T g Þ

  Pv Q evap ¼ 0:027ðΔTÞ1=3 P sat 1  P sat

ð497Þ

where ΔT is the virtual temperature difference between water and

908

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

Fig. 77. Schematic of the stepped solar still for effluent desalination [79].

Dunkle’s model. Also the expressions for glass cover temperature and instantaneous thermal efficiency were derived in terms of glass cover inclination angle (θ) and found that the solar still gives the maximum yield for an east-west orientation for θ o 551, during the winter period. In multi-basin solar stills, it is inferred that the effect of wind speed is considerable to increase the productivity. Hence it is recommended that these kinds of solar stills are highly suitable at windy regions. In multi-effect solar stills, it is found that the convective and radiative heat transfer coefficients are independent of the operating temperature range. In case of multieffected inverter absorber solar still, it is found from the analysis that seven is the optimum number of basins to obtain maximum productivity. All these models have their own advantages and disadvantages in terms of yield and operational features. For example, tubular and inverted absorber solar stills produced double the output of conventional solar still. However, all these designs had a great impenetrability in design, fabrication and operational usage. So, their real time applications need further investigations to implement in rural areas.

8. Scope for further research

air and is estimated as the temperature difference between the water temperature (Tw) and the air–vapor mixture temperature (Tmix). During the simulation study, the temperature of air–vapor mixture (Tmix) within the cavity was taken as (Tw þ2). The thickness of water film was estimated at 0.003 m, which is the thickness of the black wick. Then several simulations were performed to observe the effect of the different parameters on the condensation rate. From the experimental analysis, it was observed that when the feed water mass flow rate decreases, the condensation rate increases for the same solar intensity because less feed water enters the system. The system can generate 3.5–5.4 kg/m2/d distilled water. The temperature of the generated hot water is about 40 1C, which is good enough for domestic usage. It was concluded that the simulation results are in good agreement with the experimental results.

Solar still is a simple and economical device particularly for rural development. So far developed stills were not in use for long term operations due to various factors like material, climatic condition, water quality and end user behavior. From the above literature review, it is found that few more research areas in solar stills are unexplored due to complexity in the analysis or experimentation. The effect of salinity of water on still productivity was investigated by some researchers. But the effect of pH value, presence of minerals, total dissolved solids (TDS), turbidity, etc. of brackish water on the productivity and still efficiency are unknown. Also the solar still specific software technologies must be developed for the simulation studies. The computational fluid dynamics can be effectively utilized to analyze the dynamic behavior of brackish water on the still performance. The glass has been widely used as the condensing material in most of the solar stills. But it could not effectively transfer the latent heat of condensation accumulated in the inner space of the still to the atmosphere due to its poor thermal conductivity. This reduces the water–glass cover temperature difference and in turn reduces the yield. Flowing water on the glass cover surface is not found an effective method to reduce the glass cover temperature since it reduces the incoming solar radiation to the still basin. Also separate condensing chamber for condensation of pure water

7.3.16. Key findings and discussion on thermal models of new designs of solar still Due to poor performance of single basin single slope solar still, the researchers focused on the development of new designs to suit the required capacity of fresh water. These new designs mainly concentrated to create a modification in the basic structure of solar still like double slope, double basin, triple basin, multi-stage stacked tray, tilted wick, multi wick, inverted absorber, stepped, pyramid shaped, weir, tubular, inverted trickle, etc. Based on the structure of the solar still, the energy balances were modified and validated with experimental results. Most of these solar stills were operated under passive mode and hence the researchers predicted and validated the performance of the stills by using Dunkle’s model. In double slope solar still, the variation in transmittance of the glass cover was considered in its energy balance which reduces the error in predicting the production rate as compared with

Fig. 79. Schematic of the weir type solar still [81].

Fig. 78. Schematic of the stepped solar still with solar collector [80].

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

increases the cost and complexity in the design. Hence it is suggested that new glazy composite materials with high transmittance and having high thermal conductivity should be tested to improve the productivity. The important problem with the existing design of the solar still is the difficulty in the augmentation of various renewable energy devices to supply additional thermal energy to the basin water. Hence the still should have a provision to easily augment various energy devices to utilize the waste heat effectively. Also the size must be optimized to make the still more compact and easily transferrable. Instead of simply augmenting additional equipment to the existing passive still, the possibility of utilizing the waste heat energy available at various places like small thermal industries, waste heat energy from cooking of food items in hotels, homes, cafeterias, etc. should be explored. Sampathkumar and Senthilkumar [86] proposed a new system operated in a hybrid nature and was capable of producing hot water as well as distilled water based on the situational requirement. These types of models have an advantage of reduction in overall initial investment cost of solar distillation unit and effective utilization of the equipment augmented with it. In the literature, most of the thermal models were presented based on certain assumptions that are far away from the real operating conditions. Hence, a robust thermal model could be developed by incorporating all set of parameters. Further studies may also to be considered the economic, social, environmental, cultural, political and technical variables and their effect for implementation of solar still for real time applications.

909

All the discussed thermal models have their own advantages and limitations due to certain assumption during the development of model. The study revealed that, KTM model is more valid for active solar stills; however, the constants C and n values were predicted from the extensive experimental results. So, it may not be useful for design of solar still based on the theoretical analysis. The thermal modeling is a powerful tool that can be utilized to optimize the performance of the solar still for the given set of parameters. It will be helpful to predict the behavior of particular type of solar still to understand its suitability and techno-economic viability. The tremendous improvement in the area of software gives lot of opportunities for model testing and design changes for solar stills. Hence it is suggested that thermal models should be developed for the solar stills and the influencing parameter values must be selected by simulation methods suitable for local weather conditions before its fabrication and implementation. Based on the review conducted on various thermal models for passive and active solar stills, it is concluded that more research is needed on solar/hybrid systems especially waste heat recovery from other resources for water and power cogeneration, because both are crucial in remote areas. Worldwide interest in small residential solar still units is now growing due to the burning price of fossil fuels. Although the solar stills at present could not compete with oil-fired energy intensive desalination systems in large central plants, it will surely become a viable technology within the next few decades when the fossil fuel resource will have approached exhaustion. Also it is suggested that smaller plants consisting of solar stills, serving smaller communities in arid and rural areas will be the right application of this technology for the solar energy rich countries in future.

9. Conclusions Appendix A Solar still is an exceptional device for the production of potable water particularly for rural communities. Among the different types of solar still, single basin single slope occupied a best place due to its simplicity and design. However, because of its lower yield, scientists invented many other solar still designs for commercialization. This article reviewed the different thermal models used in passive and active solar stills and also viewed new designs of solar still in detail. The selection of particular design is based on many parameters like, economics, material availability, yield requirement, local climatic conditions, water quality and operational issues. The single common design may not be useful throughout the world due to its basic nature. The applied research carried out on solar stills were reached maximum only in laboratory conditions and only few research works have been carried out in actual field conditions. The far-reaching research on laboratory model to real model may be carried out for better understanding of the solar still application for end users.

Fig. 80. Cross sectional view of a schematic of cascade solar still [82].

Solar flux absorbed by the glass cover

α ¼ ð1  Rg Þαg 0 g

ðA1Þ

Solar flux absorbed by the water mass

α ¼ ð1  αg Þð1 Rg Þð1  Rw Þαw 0 w

ðA2Þ

Solar flux absorbed by the basin liner

α ¼ ð1  αg Þð1  Rg Þð1  Rw Þð1  αw Þαb 0 b

ðA3Þ

Temperature dependent physical properties of water–vapor and other empirical relations Vapor temperature T v ¼

T w þ T gi 2

ðA4Þ

Fig. 81. Schematic of weir type cascade solar still with phase change material (PCM) [83].

910

C. Elango et al. / Renewable and Sustainable Energy Reviews 47 (2015) 856–911

Specific heat C pf ¼ 999:2 þ ð0:1434  T v Þ þ ð1:101  10  4  T v 2 Þ ð6:7581  10  8  T v 3 Þ Density ρf ¼

353:44 ðT v þ 273:15Þ

ðA5Þ ðA6Þ

Thermal conductivity K f ¼ 0:0244 þ ð0:7673  10  4  T v Þ

ðA7Þ

Viscosity μf ¼ 1:718  10  5 þ ð4:620  10  8  T v Þ

ðA8Þ

Latent heat of vaporization hfg ¼ 3:1615  106  ½1  ð7:616  10  4  T v Þ for T v 4 70 1C

ðA9Þ

hfg ¼ 2:4935  106    4 7 2  1  9:4779  10  T v þ 1:3132  10  T v  i  4:7974  10  9  T v 3 for T v o 70 1C Expansion factor β ¼

ðA10Þ

1 ðT i þ 273:15Þ

ðA11Þ

βgd3f ρ2f ΔT μ2f

ðA12Þ

Grash of number Gr ¼

Prandtl number Pr ¼

Fig. 84. Schematic of inclined solar water distillation system [85].

μf C pf Kf

Fig. 82. Schematic of inverted trickle solar still [84].

Fig. 83. Cross sectional view of the inverted trickle solar still [84].

ðA13Þ

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