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Parametric study of a shallow solar-pond under the batch mode of heat extraction
Applied Energy 78 (2004) 159–177 www.elsevier.com/locate/apenergy
Parametric study of a shallow solar-pond under the batch mode of heat extraction S. Aboul-Enein, A.A. El-Sebaii*, M.R.I. Ramadan, A.M. Khallaf Department of Physics, Faculty of Science, Tanta University, Tanta, Egypt Received 4 June 2003; accepted 21 June 2003
Abstract In this paper, the thermal performance of a shallow solar-pond (SSP) under the batch mode of heat extraction has been investigated theoretically and experimentally. A transient mathematical model has been proposed. A computer program has been developed based on an analytical solution of the energy-balance equations of different elements of the pond. Numerical calculations have been carried out to study the effects of various configurational and operational parameters on the pond’s performance. To improve the pond’s performance, an outer mirror is hinged outside the pond to increase the amount of solar radiation incident on the pond cover. Optimization of various dimensions of the pond has been carried out. Effects of the pond’s water-depth Xw, wind speed V, the sides’ Xs and back Xb insulation thicknesses as well as the height C and width W of the outer mirror have been investigated. The influence of the number of glass covers over the pond during the night have also been studied. Comparisons between experimental and theoretical results showed that good agreement has been achieved. Experiments indicated that the pond could provide 88 l of hot water at a maximum temperature of 60 C at sunset. The pond can retain hot water till 7.00 a.m. next day at a temperature of 47 C: this is suitable for domestic applications. # 2003 Elsevier Ltd. All rights reserved. Keywords: Shallow solar ponds; Thermal performance; Heat extraction
* Corresponding author. Fax: +20-40-338-0504. E-mail address: [email protected] (A.A. El-Sebaii). 0306-2619/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2003.06.001
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Nomenclature surface area of the outer mirror (m2) surface area of the glass cover (m2) surface area of the absorber plate (m2) surface area of the sides’ insulating material (m2) surface area of the pond water (m2) width of the pond (m) height of the outer mirror (m) specific heat of water (J/kg C) convective heat-transfer coefficient between the glass cover and the ambient air (W/m2 C) hclu convective heat-transfer coefficient between the lower and upper glass covers (W/m2 C) hcpw convective heat-transfer coefficient between the absorber plate and the pond water (W/m2 C) hcua convective heat-transfer coefficient between the upper glass cover and the ambient air (W/m2 C) hcwg convective heat-transfer coefficient between the pond water and the glass cover (W/m2 C) hcwl convective heat-transfer coefficient between the pond water and the lower glass cover (W/m2 C) hrgs ; hrus radiative heat-transfer coefficient between the glass cover and the sky (W/m2 C) hrlu radiative heat-transfer coefficient between the lower and upper glass covers (W/m2 C) I solar radiation on a horizontal surface (W/m2) Ir solar radiation reflected from the mirror to the pond cover (W/m2) It total solar radiation incident on the mirror (W/m2) Kg thermal conductivity of the glass (W/m C) Ks thermal conductivity of the sides’ insulating material (W/m C) Kw thermal conductivity of the pond water (W/m C) L length of the pond (m) mw mass of the pond water (kg) Nu Nusselt number (dimensionless) Ra Rayleigh number (dimensionless) t desired time-period (s) Ta ambient-air temperature ( C) Tg glass-cover temperature ( C) Tgl lower glass-cover temperature ( C) Tgu upper glass-cover temperature ( C) Tp absorber plate temperature ( C) Ts sky temperature ( C)
Ac Ag Ap As Aw b C Cw hcga
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Tw Ub Us V W Xglu Xs Xw
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pond-water temperature ( C) bottom loss-coefficient (W/m2 C) sides’ loss coefficient (W/m2 C) wind speed (m/s) width of the outer mirror (m) distance between the lower and upper glass-covers (m) thickness of the side’s insulating material (m) depth of the pond water (m)
Greek letters g absorptivity of the glass cover p absorptivity of the absorber plate w absorptivity of the pond water "g ; "p emissivities of glass cover and absorber plate, respectively angle between the pond cover and the outer mirror (degrees) reflectance of the outer mirror Stefan-Boltzmann’s constant (W/m2 K4) g transmissivity of the glass cover w transmissivity of water
1. Introduction The shallow solar-pond (SSP) is a water-filled plastic bag placed inside an enclosure, which is insulated at the bottom and sides and covered by a clear plastic cover. The water-filled plastic bag is constructed from a lower black film and an upper clear plastic film. The depth of the water in the plastic bag is very small, generally in the range 4–15 cm. The upper clear plastic film is in contact with the water surface, so that no evaporation of water occurs, and hence, the cooling effect due to water evaporation is prevented. The temperature of the pond water is approximately inversely proportional to its depth. There are three modes of operation possible with the SSP [1]. The first mode is called the batch-heating mode in which, the pond is filled in the early morning with water at an initial temperature Twi. In the afternoon, when the water temperature reaches its maximum value, the pond is emptied into an insulating reservoir. In the second mode, which called the closed-cycle continuousflow heating mode, the water is continuously circulated at a constant rate between the pond and the storage reservoir from which heat may or may not be continuously removed by a heat exchanger. When the useful heat added to the pond water reaches zero, all of the pond water is emptied into the reservoir. The third mode is called the open-cycle continuous-flow heating-mode in which the water at the initial temperature Twi flows continuously at a constant rate through the pond and then either to storage or to some end-use. As in the closed-cycle mode, water is drained from the pond when the useful heat added to the pond reaches zero. The various aspects of the SSP suitable for domestic purposes and for supplying industrial process heat
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have been presented by Garg et al. [2]. Taga et al. [3] have designed and tested a SSP with a cover made from a transparent double film. Gonzalez et al. [4] studied theoretically and experimentally the effect of the pond’s water-depth on the pond performance throughout daytime hours in order to find the optimum depth of water. Ali [5] and Ali and Akhlaghi [6] developed a theoretical model, which was validated experimentally, to predict the performance of a SSP. Transient analysis of the SSP water heaters integrated with baffle plates has been presented by Dutt et al. [7] and Madhuri and Tiwari [8]. It is concluded that better performance of the SSP can be achieved with the use of baffle plates. Parkash et al. [9,10] have investigated the effect of using a movable insulation cover on the performance of a collector-cumstorage water-heating system. In this paper, a SSP with 1 m2 area has been investigated theoretically and experimentally under the batch mode of heat extraction. The optimum configuration and operational parameters of the SSP have been specified by computer simulation to be used in the construction of the pond. Comparisons between experimental and theoretical results have been also performed in order to validate the proposed mathematical models.
2. Construction of the pond A schematic diagram of the constructed SSP is shown in Fig. 1. It was fabricated at the Solar Energy Laboratory, Physics Department, Tanta University. A galvanized-iron sheet (0.001 m thick) was used for fabricating the pond with a depth of 0.088 m and a bottom surface area of 1 m2, which acts as the absorbing surface for the incident solar-radiation. In order to minimize the heat losses from the back and sides of the pond, a 0.05 m thick layer of sawdust is used as an insulating material. The metallic box and the insulating layer are contained in a wooden frame, which is painted white outside, to reduce the amount of solar radiation absorbed by it and to prevent deterioration of the frame by the weather. The surface of the absorber facing the sun is painted black to maximize the amount of the absorbed solar radiation. Two sheets of ordinary glass 0.003 m thick, an area of 1.0 m2 and a gap of 0.027 m in between are fixed in a wooden frame to be used as the cover for the pond. A plane mirror with an area of 1.0 m2 is hinged at the top of the pond in order to increase the amount of solar radiation incident on the pond’s cover. The outer mirror has been also used as overnight insulation by using a 0.05 m thick layer of sawdust between the back surface of the mirror and a wooden sheet. Because of the heavy weight of the mirror and its back insulation, a wooden holder is used to support the mirror with different angles between the mirror and the pond cover. Two PVC pipes connected to water taps are fixed in the holes, which are drilled in one side of the pond; one of them is used for filling the pond and the other is used for removing the overflow water. A third PVC tube, connected also to a water tap, is fixed at the pond’s bottom and is used for extracting hot water from the pond’s bottom as shown in Fig. 1. The two pipes, which are fixed at the pond side help in achievement the required good contact between the water surface and the glass
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Fig. 1. A schematic diagram of the constructed SSP with double glass covers; * thermojunction positions.
cover by the continuous addition of water in the filling pipe until the pond becomes completely filled with water; then, the excess amount of water flows through the overflow pipe. NiCr–Ni thermocouples are used to measure the temperatures at different locations of the system as indicated in Fig. 1.
3. Thermal analysis The absorber plate absorbs most of solar radiation transmitted through the glass cover(s) and pond water. The heat is transferred by convection to the pond water; so that, its temperature will be increased. The heat is then transferred by convection to the glass cover, which in turns loses energy to surroundings by convection and radiation. The mathematical model of the SSP is based on formulating the energybalance equations for various components of the pond. In order to write the energybalance equations, the following assumptions are made: (i) The heat capacities of the absorber plate, glass cover and insulation are neglected compared with that of the pond water. (ii) The glass cover is in contact with the water surface, to prevent evaporative heat transfer between the water surface and the glass cover. This assumption is justified by achieving the required good contact using the filling and
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overflow pipes. (iii) The surface areas of water, absorber plate and glass cover are equal. (iv) There is no temperature gradient across the thickness of water. This assumption is justified by taking a relatively small depth of water (0.088 m). Based on these assumptions, the energy balance equations for the different elements of the SSP under different operational and configurational conditions may be written as in the following sections. 3.1. Energy balance equations for the SSP with single glass-cover For the glass cover; Ig Ag þ hcwg Aw Tw Tg ¼ hcga Ag Tg Ta þ hrgs Ag Tg Ts
ð1Þ
where hcga is the convective heat-transfer coefficient from the glass cover to the ambient air. hcga is calculated by using the following correlation [11] hcga ¼ 2:8 þ 3:0V
ð2Þ
The sky temperature Ts is taken as the sink temperature and it is calculated using Swinbank’s formula [12] Ts ¼ 0:0052Ta1:5
ð3Þ
For the absorber plate; Ig w p Ap ¼ hcpw Ap Tp Tw þ Ub Ap Tp Ta
ð4Þ
where w is the pond water transmissivity given by the following equation [13]. w ¼
4 X
i expð i Xw Þ
ð5Þ
i¼1
where i is the extinction coefficient of the solar-radiation portion i . Ub ¼ ðKb =Xb Þ is the back-loss coefficient. Kb and Xb are the thermal conductivity and thickness of the back insulating material, respectively. For the pond water; Ig w Aw þ hcpw Ap Tp Tw ¼ mw Cw ðdTw =dtÞ þ hcwg Aw Tw Tg þ Us As ðTw Ta Þ
ð6Þ
where Us ¼ ðKs =Xs Þ is the side-loss coefficient. Rearranging Eqs. (1) and (4), one obtains Tg ¼ Ig Ag þ hcwg Aw Tw þ hcga Ag Ta þ hrgs Ag Ts = hcwg Aw þ hcga þ hrgs Ag Tp ¼ Ig w p þ hcpw Tw þ Ub Ta = hcpw þ Ub
ð7Þ
ð8Þ
On substituting Tg and Tp and using Eqs. (7) and (8), Eq. (6) may be simplified as
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MðdTw =dtÞ ¼ fðtÞ aTw
165
ð9Þ
where n fðtÞ ¼ Ig w Aw þ
Ig hcwg Ag Aw I h A þ g w p cpw p hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs hcwg hrgs Ag Aw Ts þ Ta þ hcwg Aw þ Ag hcga þ hrgs " # hcwg hcga Ag Aw hcpw Ub Ap o þ Us As þ ; hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs
a ¼ hcpw Ap þ Us As þ hcwg Aw
h2cpw Ap h2cwg Aw2 hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs
ð10Þ
ð11Þ
and M ¼ mw Cw :
ð12Þ
The solution of Eq. (9), using the initial condition Tw ðt ¼ 0Þ ¼ Twi , is Tw ¼ fðtÞ=a ½1 expðat=MÞ þ Twi ½expðat=MÞ
ð13Þ
where fðtÞ is the average value of fðtÞ for a small time-interval Dt, and it may be treated as a constant [14]. Twi is the initial temperature of the water. Analytical expressions for Tg and Tp in terms of climatic and design parameters as well as the various heat transfer coefficients can be obtained by substitution from Eq. (13) into Eqs. (7) and (8), respectively. 3.2. Energy balance equations for the SSP with double glass covers For the upper glass-cover; Ig Ag þ hclu Ag Tgl Tgu þ hrlu Ag Tgl Tgu ¼ hcua Ag Tgu Ta þ hrgs Ag Tgu Ts
ð14Þ
where hclu is the convective heat-transfer coefficient between the lower and upper glass covers. hclu is calculated by using the following Eq. [15]. hclu ¼ Nu:Kair =Xglu where Nu is the Nusselt number calculated using Holland’s correlation [16]
ð15aÞ
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Nu ¼ 1 þ 1:44 1 1708ðsin1:8 Þ1:6 =Racos þ ½1 ð1708=Racos Þ þ þ ðRacos =5380Þ1=3 1
ð15bÞ
for 0 < Ra < 105 ; 0 4 4 75o where the notation [ ]+ denoted that if the quantity inside the bracket is negative it should be equal zero. For the lower glass-cover; Ig g Ag þ hcwl Aw Tw Tgl ¼ hclu Ag Tgl Tgu þ hrlu Ag Tgl Tgu ð16Þ For the absorber plate; Ig2 w p Ap ¼ hcpw Ap Tp Tw þ Ub Ap Tp Ta For the pond water; Ig2 w Aw
þ hcpw Ap Tp Tw ¼ mw Cw
ð17Þ
dTw þ hcwl Aw Tw Tg þ Us As dt
ðTw Ta Þ From Eqs. (14), (16) and (17), Tgu ,Tgl and Tp may be written as follows Tgu ¼ Ig þ ðhclu þ hrlu ÞTgl þ hcua Ta þ hrus Ts =ðhclu þ hrlu þ hcua þ hrus Þ Tgl ¼ Ig g Ag þ hcwl Aw Tw þ ðhclu þ hrlu ÞAg Tgu = hcwl Aw þ Ag ðhclu þ hrlu Þ Tp ¼ Ig2 w p þ hcpw Tw þ Ub Ta = hcpw þ Ub
ð18Þ
ð19Þ ð20Þ
ð21Þ
On substituting Tgu , Tgl and Tp using Eqs. (19)–(21), the solution of Eq. (18) is obtained as Tw ¼ f1 ðtÞ=a ½1 expðat=MÞ þ Twi expðat=MÞ ð22Þ with
f1 ðtÞ ¼ Ig2 w Aw Ig2 w p hcpw Ap hcpw þ Ub Ig g hcwl Ag Aw h A A ðh þ hrlu ÞTgu þ cwl g w clu þ hcwl Aw þ hclu þ hrlu Ag hcwl Aw þ ðhclu þ hrlu ÞAg
hcpw Ub Ap þ Us As þ Ta hcpw þ Ub þ
a and M are given by Eqs. (11) and (12), respectively.
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The convective (hcpw and hcwg ) as well as the radiative (hrlu and hrgs ) heat-transfer coefficients are calculated using the standard methods given in the literature [17–19]. 3.3. The SSP with an outer mirror The solar radiation reflected from the mirror to the glass cover of the pond is given by [20] Ir ¼ It Ag =AC FgC ð23Þ where FgC is the view factor. FgC can be determined from the following equation. FRC ¼ ðC þ g SÞ=2g
ð24Þ
1=2 S ¼ C 2 þ g2 2Cgcos
ð25Þ
with
where C is the height of the mirror, g is the length of the glass cover; S is the distance from the outer edge of the pond to the upper edge of the mirror. The energy balance equations for the various elements of the pond with the outer mirror are similar to those given for the pond with single or double glass-covers (Sections 3.1 and 3.2), except that the solar intensity I in Eqs. (1), (4), (6), (14), (16), (17) and (18) should be written as (Ih+Ir); where, Ih is the solar radiation incident on the horizontal surface (i.e. the pond cover).
4. Experiments and numerical calculations In order to study the effect of climatic and operational parameters on the performance of the SSP, experiments have been carried out during June, July, August and September of 2001. The system is oriented to face south to maximize the solar radiation received by the pond’s cover. The global solar radiation incident on a horizontal surface is measured using an Eppley-Precession Spectral Pyranometer (EPSP) coupled to an Instantaneous Solar Radiation meter model no. 455. Calibrated NiCr–Ni thermocouples connected to a FLUKE 73 digital multimeter are used to measure the temperatures of different elements of the pond, e.g., the absorber plate, pond water and the inner and outer surfaces of the glass cover at half-hour intervals. The ambient temperature has been also recorded. Two thermocouples are fixed within the pond water at depths of 0.02 and 0.06 m, to measure the bulk temperature of the pond water. All thermocouple junctions exposed to the solar radiation are shielded with an aluminum foil in order to diminish the errors resulting from the solar radiation absorbed by the thermocouple junctions. To carry out the various experiments, two units of the pond are constructed and tested simultaneously under the same outdoor conditions. The units are filled with tap water at 7.00 a.m. and the experiments are continued until the pond water achieves its maximum temperature. The effects of the number of glass covers and using an overnight
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insulation above the glass cover of the pond on the pond’s performance has been studied. Furthermore, some experiments are carried out for several successive days with and without the overnight insulation. To investigate the storage ability of the system, some experiments are continued until the early morning of the next day. Numerical calculations are performed using suitable computer programs which are prepared by the authors for the solution of the energy-balance equations. The input parameters to the programs are climatic, design and operational parameters. Numerical calculations are initiated assuming the temperatures of the various elements of the pond to be equal to the ambient temperature at t=0. Using these temperatures, different heat-transfer coefficients are calculated. Using the values obtained for the various heat-transfer coefficients along with climatic parameters, the temperatures of the pond elements are calculated. The above procedure is repeated with the new values of different temperatures for an additional time-interval Dt and so on. The relevant parameters, which have been used for numerical calculations are given in Table 1.
5. Results and discussions The thermal performance of the SSP has been investigated experimentally and theoretically under different configurational and operational conditions. Hourly variations of solar radiation I, ambient temperature Ta and calculated temperatures of the absorber plate Tp , pond water Tw , glass cover Tg for a pond (1 m2 area) with a single glass-cover when the water depth Xw equals 0.10 m for a typical summer day are shown in Fig. 2. From the results of Fig. 2, it is seen that the solar radiation increases with the time of day to show its maximum value of 983 W/m2 at 1.00 p.m. The temperatures of the different elements of the pond (Tp , Tw and Tg ) exhibit qualitatively the same behavior as the solar radiation and they have maximum values of 46.7, 45.3 and 42.6 C, respectively, at 3.00 p.m. The peak of the solar radiation takes place 2 h earlier than those of the various temperatures due to the thermal inertia of the pond. Hourly variations of the measured solar radiation I, ambient-air temperature Ta and measured temperatures of the pond elements with double glass covers on 5 July 2001 are shown in Fig. 3. Again, the temperatures of Table 1 Numerical parameters used for numerical calculations [21,22] Relevant parameters
Numerical values
Relevant parameters
Numerical values
Ks, Kb Xb, Xs g w p Cw V
0.059 (W/m C) 0.05 m 0.9 1 w 0.95 4190 (J/kg C) 2 m/s (summer) 3 m/s (winter)
g Kw Kg Kair "g "p
0.05 0.6405 (W/m C) 0.78 (W/m C) 0.02624 (W/m C) 0.85 5.669108 (W/m2 K4) 0.88 0.85
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Fig. 2. Hourly variations of solar intensity I, ambient temperature Ta and calculated temperatures for the pond elements with a single glass-cover.
different elements of the SSP (Tp , Tw , Tgl and Tgu ) closely follow the solar-radiation behavior. The peak of solar radiation takes place 2–4 h earlier than those of the temperatures of the various elements of the pond due to the time required for the pond water to warm up. The maximum temperature of the pond water is found to lag about 1–2 and 3–4 h behind the maximum ambient-air temperature and solar radiation, respectively. The latter results agree with that outlined in previous work [5,6]. It is also clear from Fig. 3 that during the overnight period, the temperature of the lower glass-cover Tgl exceeds the temperatures of both the absorber plate Tp and pond water Tw due to the increased rate of heat transfer from the absorber plate and pond water to the lower glass-cover. To validate the proposed mathematical models, the pond has been investigated experimentally and theoretically under the same operational and climatic conditions. Fig. 4 shows comparisons between the measured and calculated temperatures of the various elements of the SSP, when the water depth equals 0.088 m with double glass-covers and an outer mirror on 12 July 2001. It is clear that there is a fairly good agreement between measured and calculated temperatures. The maximum values of the relative percentage differences between the measured and calculated values of Tp , Tw and Tgu are found to be 1.58, 0.72 and 2.5%, respectively. The differences between the measured and calculated temperatures are mainly because the temperature distribution within the pond water is neglected. The heat capacities of the absorber plate, glass covers and insulating materials are not considered in the mathematical analysis and they represent another source of error. The uncertainties in the correlations used for calculating the various heat-transfer coefficients may give some differences between measured and calculated results.
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Fig. 3. Hourly variations of solar intensity I, ambient temperature Ta and measured temperatures for the pond elements with double glass-covers.
Fig. 4. Comparisons between measured and calculated temperatures for the various elements of the pond with double glass-covers and the outer mirror.
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Since, the agreement between the measured and calculated results is found to be satisfactory, the effects of the various configurational and operational parameters on the pond performance have been studied by computer simulation. Fig. 5 shows the hourly variations of the calculated water-temperature Tw for different values of the pond’s water-depth Xw on 12 July 2001 when L=b=1.0 m. It is seen that Tw decreases with the increase of Xw during sunshine hours due to the increased heat capacity of the pond water with increasing Xw . Therefore, the peaks of Tw vs time curves are shifted toward the late afternoon. The maximum values of Tw are obtained as 80.2, 68, 60.3, 55, 51.3, 44.7 and 42.2 C when Xw equals 0.02, 0.04, 0.06, 0.08, 0.10, 0.16 and 0.20 m, respectively. Overnight, Tw is found to increase with increasing Xw as expected due to the storage effect of the pond water. The obtained results agree well with those obtained by Gonzalez et al. [4]. It is also clear from the results of Fig. 5 that the change in Tw becomes insignificant at values of Xw higher than 0.16 m. The dependence of the pond’s water-temperature Tw on the side Xs and back Xb insulation thickness is shown in Fig. 6 when Xw =0.10 m on a summer day (12 July 2001). Tw is less dependent on the insulation thickness during sunshine hours. However, Tw is found to increase with an increase of Xs and/or Xb during offsunshine hours until typical values for these parameters are achieved. A typical value of the insulation thickness is found to be 0.04 m beyond which the increase in Tw with an increase’s of Xs and Xb is insignificant. Numerical calculations have also been performed to optimize the height C and width W of the mirror. Variations of the calculated Tw for different values of C and W are shown in Fig. 7(a) and (b), respectively. It is seen from the results of Fig. 7(a) that the mirror height C has a
Fig. 5. Calculated pond’s water-temperature Tw vs. time for different depths Xw of the pond water.
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Fig. 6. Calculated pond’s water-temperature Tw vs. time for different thicknesses of the side Xs and back Xb insulating material.
marginal effect on Tw . However, Tw is found to increase upon increasing the mirror width W, especially during the period from noon until sunset as is shown in Fig. 7(b). The maximum value of Tw is found to increase from 54.3 to 58.2 C on increasing W from 0.5 to 2.5 m. Increasing W beyond 2.5 m has no effect on Tw . On the basis of the results of Fig. 7(a) and (b), the geometric concentration ratio of the pond, which is defined as the ratio between the mirror width W and the pond width, is found to be 2.5. There is no benefit in increasing the geometric concentration-ratio beyond this value. This agrees with data obtained for the box-type solar cooker, investigated theoretically and experimentally under Cairo weather conditions [23]. The dependences of the calculated Tw on the wind speed V for the SSP with single and double glass-covers are shown in Fig. 8(a) and (b), respectively. When the pond is used with a single glass-cover (Fig. 8(a)), Tw decreases as V increases until a typical value of V (5 m/s) beyond which the decrease in Tw becomes insignificant. The decrease in Tw with increasing V is due to the increased heat losses by forced convection through the top of the pond. However, with double glass-covers Tw is found to decrease slightly overnight with increasing V (See Fig. 8(b)). Comparing Fig. 8(a) and (b), it can be concluded that it is advisable to use the pond with double glass-covers to reduce the heat losses from the top of the pond. The effect of using the outer mirror on Tw has also been studied experimentally using two units of the SSP one with single and the other with double glass-covers. Variations of the measured Tw with time for the pond with single and double glasscovers, with and without the outer mirror, are presented in Fig. 9. From the results of Fig. 9, it is clear that the pest performance of the SSP is obtained when the pond
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is used with double glass-covers and an outer reflector. For the case with double glass-covers, the maximum values of Tw are obtained as 55.5 and 50 C with and without the outer mirror, respectively. The results of Fig. 9 are expected because using an additional glass-sheet at the top of the pond decrease the convective and
Fig. 7. (a) Dependence of the pond’s water-temperature Tw on the height of the mirror C; (b) variations of the pond’s water-temperature Tw with time for different values of the mirror width W.
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radiative heat-losses significantly. Furthermore, the amount of solar radiation incident on the pond cover increases on using the outer mirror. The thermal performance of the SSP for several successive days without heat withdrawn has been investigated. Fig. 10 shows the hourly variations of the measured Tw with and without the night
Fig. 8. (a) Calculated pond’s water-temperature Tw vs time for different values of the wind speed V (m/s) when the pond is used with a single glass-cover; (b) same as for (a), but for the pond with double glass-covers.
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Fig. 9. Hourly variations of the measured Tw for the pond with single and double glass covers, with and without the outer mirror.
Fig. 10. Hourly variations of the measured Tw for the pond with and without the overnight insulation for four successive days (14–17 July 2001).
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insulation on 14–17 July 2001. From the results of Fig. 10, it is seen that Tw for the case with the night insulation is considerably higher than the case without the night insulation. The maximum value of Tw has been achieved on the second day for the two cases. Maximum values of Tw are obtained as 67 and 54 C with and without the night insulation, respectively. The results of Fig. 10 also indicate that the highest value of the water temperature (Tw=65 C) for the successive operation of the SSP can be achieved after two days, when the pond is covered during the night period. These results agree well with those concluded by Parkash et al. [10].
6. Conclusions On the basis of the previous theoretical and experimental investigations which have been performed on the constructed SSP under the batch mode of heat extraction, it can be concluded that the best performance of the pond can be achieved when the pond is used with double glass-covers and an outer mirror with the mirror tilt angle adjusted every half-hour. Covering the pond during the night has a great effect on the successive operation of the pond. Under the optimum operational conditions and using the batch mode of heat extraction, experiments showed that in 88 l of water is obtained at a maximum temperature of about 60 C at sunset. The same amount of water is obtained at 47 C in the early morning of the next day and which can be used for most domestic applications. The main parameter which affects the SSP performance is the water depth Xw. It is found that Tw decreases with an increase of Xw during sunshine hours and this behavior is reversed overnight. An improvement in the pond’s performance has been achieved on using an outer mirror hinged at the top of the pond. It is indicated that the mirror height has a marginal effect on Tw . However, Tw is found to increase with the increase of the mirror width especially during the period from noon until sunset.
References [1] Garg HP. Advances in solar energy technology. Vol.I. Dordecht, Holland: Reidel ; 1987 [chapter 3]. [2] Garg HP, Bandyopadhyay B, Rani U, Hrishikesan. Shallow solar ponds: state-of-the-art. Energy Convers Mgmt 1982;22:117–31. [3] Taga M, Fujimoto K, Ochi T. Field testing on non-salt solar ponds. Solar Energy 1996;56(3):267–77. [4] Gonzalez J, Perez LR, Benitez J. Modeling the thermal process in a shallow solar-pond’s water heater. Solar Energy 1992;48(4):261–5. [5] Ali HM. Study on shallow solar-pond applications at Tehran. Energy Convers Mgmt 1987;27(1):33–8. [6] Ali HM, Akhlaghi M. Experimental study in a shallow solar-pond. Solar Wind Technol 1987;4(4): 425–30. [7] Dutt DK, Rai SN, Tiwari GN. Transient analysis of a shallow solar-pond water heater integrated with a baffle plate. Energy Convers Mgmt 1987;27(3):303–7. [8] Madhuri, Tiwari GN. The effect of a baffle plate on the transient performance of a shallow solarpond’s water. Energy Convers Mgmt 1986;26(7):217–20.
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[9] Parkash J, Garg HP, Hrishikesan DS, Ranjana JHA. Performance studies of an integrated solar collector-cum-storage water-heating system with transparent insulation cover. Solar Wind Technol 1989;6(2):171–6. [10] Parkash J, Garg HP, Datta G. Performance prediction for a built-in-storage-type solar water-heater. Energy 1985;10(11):1209–13. [11] Wattmuf JH, Carter WWS, Proctor D. Solar and wind induced external coefficients for solar collectors. Comples 1977;2. [12] Swinbank WC. Long-wave radiation from clear skies. QJR Meteorol Soc 1963;89. [13] Rabl A, Nielsen CE. Solar ponds for space heating. Solar Energy 1975;17:1–12. [14] Singh AK, Tiwari GN. Thermal evaluation of regeneration active solar distillation under thermosyphon mode. Energy Convers Mgmt 1993;34:697–709. [15] Garg H.P. Treatise on solar energy, Vol. I: Fundamentals of solar energy. New York: John Wiley & Sons; 1982 [chapter 3] [16] Hollands KGT, Unny TE, Raithby GR, Konicek L. J Heat Transfer 1976;98:189–93. [17] Fishenden M, Saunders OA. An introduction to heat transfer. Oxford: University Press; 1950. [18] McAdams WH. Heat transmission. McGraw-Hill 1954. [19] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley & Sons; 1980 [chapter 6] [20] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. New York: John Wiley & Sons; 1991. [21] Tiwari GN, Sangeeta Suneja. Solar thermal engineering systems. London: Narosa Publishing House; 1997. [22] Wong HY. Heat transfer for engineers. New York: Longman; 1997 [chapter 3] [23] Metias MZ. Mathematical modeling of solar-concentrator systems: solar-box cooker. M. Sc thesis, Cairo University, 1992.
Parametric study of a shallow solar-pond under the batch mode of heat extraction S. Aboul-Enein, A.A. El-Sebaii*, M.R.I. Ramadan, A.M. Khallaf Department of Physics, Faculty of Science, Tanta University, Tanta, Egypt Received 4 June 2003; accepted 21 June 2003
Abstract In this paper, the thermal performance of a shallow solar-pond (SSP) under the batch mode of heat extraction has been investigated theoretically and experimentally. A transient mathematical model has been proposed. A computer program has been developed based on an analytical solution of the energy-balance equations of different elements of the pond. Numerical calculations have been carried out to study the effects of various configurational and operational parameters on the pond’s performance. To improve the pond’s performance, an outer mirror is hinged outside the pond to increase the amount of solar radiation incident on the pond cover. Optimization of various dimensions of the pond has been carried out. Effects of the pond’s water-depth Xw, wind speed V, the sides’ Xs and back Xb insulation thicknesses as well as the height C and width W of the outer mirror have been investigated. The influence of the number of glass covers over the pond during the night have also been studied. Comparisons between experimental and theoretical results showed that good agreement has been achieved. Experiments indicated that the pond could provide 88 l of hot water at a maximum temperature of 60 C at sunset. The pond can retain hot water till 7.00 a.m. next day at a temperature of 47 C: this is suitable for domestic applications. # 2003 Elsevier Ltd. All rights reserved. Keywords: Shallow solar ponds; Thermal performance; Heat extraction
* Corresponding author. Fax: +20-40-338-0504. E-mail address: [email protected] (A.A. El-Sebaii). 0306-2619/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2003.06.001
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Nomenclature surface area of the outer mirror (m2) surface area of the glass cover (m2) surface area of the absorber plate (m2) surface area of the sides’ insulating material (m2) surface area of the pond water (m2) width of the pond (m) height of the outer mirror (m) specific heat of water (J/kg C) convective heat-transfer coefficient between the glass cover and the ambient air (W/m2 C) hclu convective heat-transfer coefficient between the lower and upper glass covers (W/m2 C) hcpw convective heat-transfer coefficient between the absorber plate and the pond water (W/m2 C) hcua convective heat-transfer coefficient between the upper glass cover and the ambient air (W/m2 C) hcwg convective heat-transfer coefficient between the pond water and the glass cover (W/m2 C) hcwl convective heat-transfer coefficient between the pond water and the lower glass cover (W/m2 C) hrgs ; hrus radiative heat-transfer coefficient between the glass cover and the sky (W/m2 C) hrlu radiative heat-transfer coefficient between the lower and upper glass covers (W/m2 C) I solar radiation on a horizontal surface (W/m2) Ir solar radiation reflected from the mirror to the pond cover (W/m2) It total solar radiation incident on the mirror (W/m2) Kg thermal conductivity of the glass (W/m C) Ks thermal conductivity of the sides’ insulating material (W/m C) Kw thermal conductivity of the pond water (W/m C) L length of the pond (m) mw mass of the pond water (kg) Nu Nusselt number (dimensionless) Ra Rayleigh number (dimensionless) t desired time-period (s) Ta ambient-air temperature ( C) Tg glass-cover temperature ( C) Tgl lower glass-cover temperature ( C) Tgu upper glass-cover temperature ( C) Tp absorber plate temperature ( C) Ts sky temperature ( C)
Ac Ag Ap As Aw b C Cw hcga
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Tw Ub Us V W Xglu Xs Xw
161
pond-water temperature ( C) bottom loss-coefficient (W/m2 C) sides’ loss coefficient (W/m2 C) wind speed (m/s) width of the outer mirror (m) distance between the lower and upper glass-covers (m) thickness of the side’s insulating material (m) depth of the pond water (m)
Greek letters g absorptivity of the glass cover p absorptivity of the absorber plate w absorptivity of the pond water "g ; "p emissivities of glass cover and absorber plate, respectively angle between the pond cover and the outer mirror (degrees) reflectance of the outer mirror Stefan-Boltzmann’s constant (W/m2 K4) g transmissivity of the glass cover w transmissivity of water
1. Introduction The shallow solar-pond (SSP) is a water-filled plastic bag placed inside an enclosure, which is insulated at the bottom and sides and covered by a clear plastic cover. The water-filled plastic bag is constructed from a lower black film and an upper clear plastic film. The depth of the water in the plastic bag is very small, generally in the range 4–15 cm. The upper clear plastic film is in contact with the water surface, so that no evaporation of water occurs, and hence, the cooling effect due to water evaporation is prevented. The temperature of the pond water is approximately inversely proportional to its depth. There are three modes of operation possible with the SSP [1]. The first mode is called the batch-heating mode in which, the pond is filled in the early morning with water at an initial temperature Twi. In the afternoon, when the water temperature reaches its maximum value, the pond is emptied into an insulating reservoir. In the second mode, which called the closed-cycle continuousflow heating mode, the water is continuously circulated at a constant rate between the pond and the storage reservoir from which heat may or may not be continuously removed by a heat exchanger. When the useful heat added to the pond water reaches zero, all of the pond water is emptied into the reservoir. The third mode is called the open-cycle continuous-flow heating-mode in which the water at the initial temperature Twi flows continuously at a constant rate through the pond and then either to storage or to some end-use. As in the closed-cycle mode, water is drained from the pond when the useful heat added to the pond reaches zero. The various aspects of the SSP suitable for domestic purposes and for supplying industrial process heat
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have been presented by Garg et al. [2]. Taga et al. [3] have designed and tested a SSP with a cover made from a transparent double film. Gonzalez et al. [4] studied theoretically and experimentally the effect of the pond’s water-depth on the pond performance throughout daytime hours in order to find the optimum depth of water. Ali [5] and Ali and Akhlaghi [6] developed a theoretical model, which was validated experimentally, to predict the performance of a SSP. Transient analysis of the SSP water heaters integrated with baffle plates has been presented by Dutt et al. [7] and Madhuri and Tiwari [8]. It is concluded that better performance of the SSP can be achieved with the use of baffle plates. Parkash et al. [9,10] have investigated the effect of using a movable insulation cover on the performance of a collector-cumstorage water-heating system. In this paper, a SSP with 1 m2 area has been investigated theoretically and experimentally under the batch mode of heat extraction. The optimum configuration and operational parameters of the SSP have been specified by computer simulation to be used in the construction of the pond. Comparisons between experimental and theoretical results have been also performed in order to validate the proposed mathematical models.
2. Construction of the pond A schematic diagram of the constructed SSP is shown in Fig. 1. It was fabricated at the Solar Energy Laboratory, Physics Department, Tanta University. A galvanized-iron sheet (0.001 m thick) was used for fabricating the pond with a depth of 0.088 m and a bottom surface area of 1 m2, which acts as the absorbing surface for the incident solar-radiation. In order to minimize the heat losses from the back and sides of the pond, a 0.05 m thick layer of sawdust is used as an insulating material. The metallic box and the insulating layer are contained in a wooden frame, which is painted white outside, to reduce the amount of solar radiation absorbed by it and to prevent deterioration of the frame by the weather. The surface of the absorber facing the sun is painted black to maximize the amount of the absorbed solar radiation. Two sheets of ordinary glass 0.003 m thick, an area of 1.0 m2 and a gap of 0.027 m in between are fixed in a wooden frame to be used as the cover for the pond. A plane mirror with an area of 1.0 m2 is hinged at the top of the pond in order to increase the amount of solar radiation incident on the pond’s cover. The outer mirror has been also used as overnight insulation by using a 0.05 m thick layer of sawdust between the back surface of the mirror and a wooden sheet. Because of the heavy weight of the mirror and its back insulation, a wooden holder is used to support the mirror with different angles between the mirror and the pond cover. Two PVC pipes connected to water taps are fixed in the holes, which are drilled in one side of the pond; one of them is used for filling the pond and the other is used for removing the overflow water. A third PVC tube, connected also to a water tap, is fixed at the pond’s bottom and is used for extracting hot water from the pond’s bottom as shown in Fig. 1. The two pipes, which are fixed at the pond side help in achievement the required good contact between the water surface and the glass
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Fig. 1. A schematic diagram of the constructed SSP with double glass covers; * thermojunction positions.
cover by the continuous addition of water in the filling pipe until the pond becomes completely filled with water; then, the excess amount of water flows through the overflow pipe. NiCr–Ni thermocouples are used to measure the temperatures at different locations of the system as indicated in Fig. 1.
3. Thermal analysis The absorber plate absorbs most of solar radiation transmitted through the glass cover(s) and pond water. The heat is transferred by convection to the pond water; so that, its temperature will be increased. The heat is then transferred by convection to the glass cover, which in turns loses energy to surroundings by convection and radiation. The mathematical model of the SSP is based on formulating the energybalance equations for various components of the pond. In order to write the energybalance equations, the following assumptions are made: (i) The heat capacities of the absorber plate, glass cover and insulation are neglected compared with that of the pond water. (ii) The glass cover is in contact with the water surface, to prevent evaporative heat transfer between the water surface and the glass cover. This assumption is justified by achieving the required good contact using the filling and
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overflow pipes. (iii) The surface areas of water, absorber plate and glass cover are equal. (iv) There is no temperature gradient across the thickness of water. This assumption is justified by taking a relatively small depth of water (0.088 m). Based on these assumptions, the energy balance equations for the different elements of the SSP under different operational and configurational conditions may be written as in the following sections. 3.1. Energy balance equations for the SSP with single glass-cover For the glass cover; Ig Ag þ hcwg Aw Tw Tg ¼ hcga Ag Tg Ta þ hrgs Ag Tg Ts
ð1Þ
where hcga is the convective heat-transfer coefficient from the glass cover to the ambient air. hcga is calculated by using the following correlation [11] hcga ¼ 2:8 þ 3:0V
ð2Þ
The sky temperature Ts is taken as the sink temperature and it is calculated using Swinbank’s formula [12] Ts ¼ 0:0052Ta1:5
ð3Þ
For the absorber plate; Ig w p Ap ¼ hcpw Ap Tp Tw þ Ub Ap Tp Ta
ð4Þ
where w is the pond water transmissivity given by the following equation [13]. w ¼
4 X
i expð i Xw Þ
ð5Þ
i¼1
where i is the extinction coefficient of the solar-radiation portion i . Ub ¼ ðKb =Xb Þ is the back-loss coefficient. Kb and Xb are the thermal conductivity and thickness of the back insulating material, respectively. For the pond water; Ig w Aw þ hcpw Ap Tp Tw ¼ mw Cw ðdTw =dtÞ þ hcwg Aw Tw Tg þ Us As ðTw Ta Þ
ð6Þ
where Us ¼ ðKs =Xs Þ is the side-loss coefficient. Rearranging Eqs. (1) and (4), one obtains Tg ¼ Ig Ag þ hcwg Aw Tw þ hcga Ag Ta þ hrgs Ag Ts = hcwg Aw þ hcga þ hrgs Ag Tp ¼ Ig w p þ hcpw Tw þ Ub Ta = hcpw þ Ub
ð7Þ
ð8Þ
On substituting Tg and Tp and using Eqs. (7) and (8), Eq. (6) may be simplified as
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MðdTw =dtÞ ¼ fðtÞ aTw
165
ð9Þ
where n fðtÞ ¼ Ig w Aw þ
Ig hcwg Ag Aw I h A þ g w p cpw p hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs hcwg hrgs Ag Aw Ts þ Ta þ hcwg Aw þ Ag hcga þ hrgs " # hcwg hcga Ag Aw hcpw Ub Ap o þ Us As þ ; hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs
a ¼ hcpw Ap þ Us As þ hcwg Aw
h2cpw Ap h2cwg Aw2 hcpw þ Ub hcwg Aw þ Ag hcga þ hrgs
ð10Þ
ð11Þ
and M ¼ mw Cw :
ð12Þ
The solution of Eq. (9), using the initial condition Tw ðt ¼ 0Þ ¼ Twi , is Tw ¼ fðtÞ=a ½1 expðat=MÞ þ Twi ½expðat=MÞ
ð13Þ
where fðtÞ is the average value of fðtÞ for a small time-interval Dt, and it may be treated as a constant [14]. Twi is the initial temperature of the water. Analytical expressions for Tg and Tp in terms of climatic and design parameters as well as the various heat transfer coefficients can be obtained by substitution from Eq. (13) into Eqs. (7) and (8), respectively. 3.2. Energy balance equations for the SSP with double glass covers For the upper glass-cover; Ig Ag þ hclu Ag Tgl Tgu þ hrlu Ag Tgl Tgu ¼ hcua Ag Tgu Ta þ hrgs Ag Tgu Ts
ð14Þ
where hclu is the convective heat-transfer coefficient between the lower and upper glass covers. hclu is calculated by using the following Eq. [15]. hclu ¼ Nu:Kair =Xglu where Nu is the Nusselt number calculated using Holland’s correlation [16]
ð15aÞ
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Nu ¼ 1 þ 1:44 1 1708ðsin1:8 Þ1:6 =Racos þ ½1 ð1708=Racos Þ þ þ ðRacos =5380Þ1=3 1
ð15bÞ
for 0 < Ra < 105 ; 0 4 4 75o where the notation [ ]+ denoted that if the quantity inside the bracket is negative it should be equal zero. For the lower glass-cover; Ig g Ag þ hcwl Aw Tw Tgl ¼ hclu Ag Tgl Tgu þ hrlu Ag Tgl Tgu ð16Þ For the absorber plate; Ig2 w p Ap ¼ hcpw Ap Tp Tw þ Ub Ap Tp Ta For the pond water; Ig2 w Aw
þ hcpw Ap Tp Tw ¼ mw Cw
ð17Þ
dTw þ hcwl Aw Tw Tg þ Us As dt
ðTw Ta Þ From Eqs. (14), (16) and (17), Tgu ,Tgl and Tp may be written as follows Tgu ¼ Ig þ ðhclu þ hrlu ÞTgl þ hcua Ta þ hrus Ts =ðhclu þ hrlu þ hcua þ hrus Þ Tgl ¼ Ig g Ag þ hcwl Aw Tw þ ðhclu þ hrlu ÞAg Tgu = hcwl Aw þ Ag ðhclu þ hrlu Þ Tp ¼ Ig2 w p þ hcpw Tw þ Ub Ta = hcpw þ Ub
ð18Þ
ð19Þ ð20Þ
ð21Þ
On substituting Tgu , Tgl and Tp using Eqs. (19)–(21), the solution of Eq. (18) is obtained as Tw ¼ f1 ðtÞ=a ½1 expðat=MÞ þ Twi expðat=MÞ ð22Þ with
f1 ðtÞ ¼ Ig2 w Aw Ig2 w p hcpw Ap hcpw þ Ub Ig g hcwl Ag Aw h A A ðh þ hrlu ÞTgu þ cwl g w clu þ hcwl Aw þ hclu þ hrlu Ag hcwl Aw þ ðhclu þ hrlu ÞAg
hcpw Ub Ap þ Us As þ Ta hcpw þ Ub þ
a and M are given by Eqs. (11) and (12), respectively.
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The convective (hcpw and hcwg ) as well as the radiative (hrlu and hrgs ) heat-transfer coefficients are calculated using the standard methods given in the literature [17–19]. 3.3. The SSP with an outer mirror The solar radiation reflected from the mirror to the glass cover of the pond is given by [20] Ir ¼ It Ag =AC FgC ð23Þ where FgC is the view factor. FgC can be determined from the following equation. FRC ¼ ðC þ g SÞ=2g
ð24Þ
1=2 S ¼ C 2 þ g2 2Cgcos
ð25Þ
with
where C is the height of the mirror, g is the length of the glass cover; S is the distance from the outer edge of the pond to the upper edge of the mirror. The energy balance equations for the various elements of the pond with the outer mirror are similar to those given for the pond with single or double glass-covers (Sections 3.1 and 3.2), except that the solar intensity I in Eqs. (1), (4), (6), (14), (16), (17) and (18) should be written as (Ih+Ir); where, Ih is the solar radiation incident on the horizontal surface (i.e. the pond cover).
4. Experiments and numerical calculations In order to study the effect of climatic and operational parameters on the performance of the SSP, experiments have been carried out during June, July, August and September of 2001. The system is oriented to face south to maximize the solar radiation received by the pond’s cover. The global solar radiation incident on a horizontal surface is measured using an Eppley-Precession Spectral Pyranometer (EPSP) coupled to an Instantaneous Solar Radiation meter model no. 455. Calibrated NiCr–Ni thermocouples connected to a FLUKE 73 digital multimeter are used to measure the temperatures of different elements of the pond, e.g., the absorber plate, pond water and the inner and outer surfaces of the glass cover at half-hour intervals. The ambient temperature has been also recorded. Two thermocouples are fixed within the pond water at depths of 0.02 and 0.06 m, to measure the bulk temperature of the pond water. All thermocouple junctions exposed to the solar radiation are shielded with an aluminum foil in order to diminish the errors resulting from the solar radiation absorbed by the thermocouple junctions. To carry out the various experiments, two units of the pond are constructed and tested simultaneously under the same outdoor conditions. The units are filled with tap water at 7.00 a.m. and the experiments are continued until the pond water achieves its maximum temperature. The effects of the number of glass covers and using an overnight
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insulation above the glass cover of the pond on the pond’s performance has been studied. Furthermore, some experiments are carried out for several successive days with and without the overnight insulation. To investigate the storage ability of the system, some experiments are continued until the early morning of the next day. Numerical calculations are performed using suitable computer programs which are prepared by the authors for the solution of the energy-balance equations. The input parameters to the programs are climatic, design and operational parameters. Numerical calculations are initiated assuming the temperatures of the various elements of the pond to be equal to the ambient temperature at t=0. Using these temperatures, different heat-transfer coefficients are calculated. Using the values obtained for the various heat-transfer coefficients along with climatic parameters, the temperatures of the pond elements are calculated. The above procedure is repeated with the new values of different temperatures for an additional time-interval Dt and so on. The relevant parameters, which have been used for numerical calculations are given in Table 1.
5. Results and discussions The thermal performance of the SSP has been investigated experimentally and theoretically under different configurational and operational conditions. Hourly variations of solar radiation I, ambient temperature Ta and calculated temperatures of the absorber plate Tp , pond water Tw , glass cover Tg for a pond (1 m2 area) with a single glass-cover when the water depth Xw equals 0.10 m for a typical summer day are shown in Fig. 2. From the results of Fig. 2, it is seen that the solar radiation increases with the time of day to show its maximum value of 983 W/m2 at 1.00 p.m. The temperatures of the different elements of the pond (Tp , Tw and Tg ) exhibit qualitatively the same behavior as the solar radiation and they have maximum values of 46.7, 45.3 and 42.6 C, respectively, at 3.00 p.m. The peak of the solar radiation takes place 2 h earlier than those of the various temperatures due to the thermal inertia of the pond. Hourly variations of the measured solar radiation I, ambient-air temperature Ta and measured temperatures of the pond elements with double glass covers on 5 July 2001 are shown in Fig. 3. Again, the temperatures of Table 1 Numerical parameters used for numerical calculations [21,22] Relevant parameters
Numerical values
Relevant parameters
Numerical values
Ks, Kb Xb, Xs g w p Cw V
0.059 (W/m C) 0.05 m 0.9 1 w 0.95 4190 (J/kg C) 2 m/s (summer) 3 m/s (winter)
g Kw Kg Kair "g "p
0.05 0.6405 (W/m C) 0.78 (W/m C) 0.02624 (W/m C) 0.85 5.669108 (W/m2 K4) 0.88 0.85
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Fig. 2. Hourly variations of solar intensity I, ambient temperature Ta and calculated temperatures for the pond elements with a single glass-cover.
different elements of the SSP (Tp , Tw , Tgl and Tgu ) closely follow the solar-radiation behavior. The peak of solar radiation takes place 2–4 h earlier than those of the temperatures of the various elements of the pond due to the time required for the pond water to warm up. The maximum temperature of the pond water is found to lag about 1–2 and 3–4 h behind the maximum ambient-air temperature and solar radiation, respectively. The latter results agree with that outlined in previous work [5,6]. It is also clear from Fig. 3 that during the overnight period, the temperature of the lower glass-cover Tgl exceeds the temperatures of both the absorber plate Tp and pond water Tw due to the increased rate of heat transfer from the absorber plate and pond water to the lower glass-cover. To validate the proposed mathematical models, the pond has been investigated experimentally and theoretically under the same operational and climatic conditions. Fig. 4 shows comparisons between the measured and calculated temperatures of the various elements of the SSP, when the water depth equals 0.088 m with double glass-covers and an outer mirror on 12 July 2001. It is clear that there is a fairly good agreement between measured and calculated temperatures. The maximum values of the relative percentage differences between the measured and calculated values of Tp , Tw and Tgu are found to be 1.58, 0.72 and 2.5%, respectively. The differences between the measured and calculated temperatures are mainly because the temperature distribution within the pond water is neglected. The heat capacities of the absorber plate, glass covers and insulating materials are not considered in the mathematical analysis and they represent another source of error. The uncertainties in the correlations used for calculating the various heat-transfer coefficients may give some differences between measured and calculated results.
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Fig. 3. Hourly variations of solar intensity I, ambient temperature Ta and measured temperatures for the pond elements with double glass-covers.
Fig. 4. Comparisons between measured and calculated temperatures for the various elements of the pond with double glass-covers and the outer mirror.
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Since, the agreement between the measured and calculated results is found to be satisfactory, the effects of the various configurational and operational parameters on the pond performance have been studied by computer simulation. Fig. 5 shows the hourly variations of the calculated water-temperature Tw for different values of the pond’s water-depth Xw on 12 July 2001 when L=b=1.0 m. It is seen that Tw decreases with the increase of Xw during sunshine hours due to the increased heat capacity of the pond water with increasing Xw . Therefore, the peaks of Tw vs time curves are shifted toward the late afternoon. The maximum values of Tw are obtained as 80.2, 68, 60.3, 55, 51.3, 44.7 and 42.2 C when Xw equals 0.02, 0.04, 0.06, 0.08, 0.10, 0.16 and 0.20 m, respectively. Overnight, Tw is found to increase with increasing Xw as expected due to the storage effect of the pond water. The obtained results agree well with those obtained by Gonzalez et al. [4]. It is also clear from the results of Fig. 5 that the change in Tw becomes insignificant at values of Xw higher than 0.16 m. The dependence of the pond’s water-temperature Tw on the side Xs and back Xb insulation thickness is shown in Fig. 6 when Xw =0.10 m on a summer day (12 July 2001). Tw is less dependent on the insulation thickness during sunshine hours. However, Tw is found to increase with an increase of Xs and/or Xb during offsunshine hours until typical values for these parameters are achieved. A typical value of the insulation thickness is found to be 0.04 m beyond which the increase in Tw with an increase’s of Xs and Xb is insignificant. Numerical calculations have also been performed to optimize the height C and width W of the mirror. Variations of the calculated Tw for different values of C and W are shown in Fig. 7(a) and (b), respectively. It is seen from the results of Fig. 7(a) that the mirror height C has a
Fig. 5. Calculated pond’s water-temperature Tw vs. time for different depths Xw of the pond water.
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Fig. 6. Calculated pond’s water-temperature Tw vs. time for different thicknesses of the side Xs and back Xb insulating material.
marginal effect on Tw . However, Tw is found to increase upon increasing the mirror width W, especially during the period from noon until sunset as is shown in Fig. 7(b). The maximum value of Tw is found to increase from 54.3 to 58.2 C on increasing W from 0.5 to 2.5 m. Increasing W beyond 2.5 m has no effect on Tw . On the basis of the results of Fig. 7(a) and (b), the geometric concentration ratio of the pond, which is defined as the ratio between the mirror width W and the pond width, is found to be 2.5. There is no benefit in increasing the geometric concentration-ratio beyond this value. This agrees with data obtained for the box-type solar cooker, investigated theoretically and experimentally under Cairo weather conditions [23]. The dependences of the calculated Tw on the wind speed V for the SSP with single and double glass-covers are shown in Fig. 8(a) and (b), respectively. When the pond is used with a single glass-cover (Fig. 8(a)), Tw decreases as V increases until a typical value of V (5 m/s) beyond which the decrease in Tw becomes insignificant. The decrease in Tw with increasing V is due to the increased heat losses by forced convection through the top of the pond. However, with double glass-covers Tw is found to decrease slightly overnight with increasing V (See Fig. 8(b)). Comparing Fig. 8(a) and (b), it can be concluded that it is advisable to use the pond with double glass-covers to reduce the heat losses from the top of the pond. The effect of using the outer mirror on Tw has also been studied experimentally using two units of the SSP one with single and the other with double glass-covers. Variations of the measured Tw with time for the pond with single and double glasscovers, with and without the outer mirror, are presented in Fig. 9. From the results of Fig. 9, it is clear that the pest performance of the SSP is obtained when the pond
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is used with double glass-covers and an outer reflector. For the case with double glass-covers, the maximum values of Tw are obtained as 55.5 and 50 C with and without the outer mirror, respectively. The results of Fig. 9 are expected because using an additional glass-sheet at the top of the pond decrease the convective and
Fig. 7. (a) Dependence of the pond’s water-temperature Tw on the height of the mirror C; (b) variations of the pond’s water-temperature Tw with time for different values of the mirror width W.
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radiative heat-losses significantly. Furthermore, the amount of solar radiation incident on the pond cover increases on using the outer mirror. The thermal performance of the SSP for several successive days without heat withdrawn has been investigated. Fig. 10 shows the hourly variations of the measured Tw with and without the night
Fig. 8. (a) Calculated pond’s water-temperature Tw vs time for different values of the wind speed V (m/s) when the pond is used with a single glass-cover; (b) same as for (a), but for the pond with double glass-covers.
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Fig. 9. Hourly variations of the measured Tw for the pond with single and double glass covers, with and without the outer mirror.
Fig. 10. Hourly variations of the measured Tw for the pond with and without the overnight insulation for four successive days (14–17 July 2001).
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insulation on 14–17 July 2001. From the results of Fig. 10, it is seen that Tw for the case with the night insulation is considerably higher than the case without the night insulation. The maximum value of Tw has been achieved on the second day for the two cases. Maximum values of Tw are obtained as 67 and 54 C with and without the night insulation, respectively. The results of Fig. 10 also indicate that the highest value of the water temperature (Tw=65 C) for the successive operation of the SSP can be achieved after two days, when the pond is covered during the night period. These results agree well with those concluded by Parkash et al. [10].
6. Conclusions On the basis of the previous theoretical and experimental investigations which have been performed on the constructed SSP under the batch mode of heat extraction, it can be concluded that the best performance of the pond can be achieved when the pond is used with double glass-covers and an outer mirror with the mirror tilt angle adjusted every half-hour. Covering the pond during the night has a great effect on the successive operation of the pond. Under the optimum operational conditions and using the batch mode of heat extraction, experiments showed that in 88 l of water is obtained at a maximum temperature of about 60 C at sunset. The same amount of water is obtained at 47 C in the early morning of the next day and which can be used for most domestic applications. The main parameter which affects the SSP performance is the water depth Xw. It is found that Tw decreases with an increase of Xw during sunshine hours and this behavior is reversed overnight. An improvement in the pond’s performance has been achieved on using an outer mirror hinged at the top of the pond. It is indicated that the mirror height has a marginal effect on Tw . However, Tw is found to increase with the increase of the mirror width especially during the period from noon until sunset.
References [1] Garg HP. Advances in solar energy technology. Vol.I. Dordecht, Holland: Reidel ; 1987 [chapter 3]. [2] Garg HP, Bandyopadhyay B, Rani U, Hrishikesan. Shallow solar ponds: state-of-the-art. Energy Convers Mgmt 1982;22:117–31. [3] Taga M, Fujimoto K, Ochi T. Field testing on non-salt solar ponds. Solar Energy 1996;56(3):267–77. [4] Gonzalez J, Perez LR, Benitez J. Modeling the thermal process in a shallow solar-pond’s water heater. Solar Energy 1992;48(4):261–5. [5] Ali HM. Study on shallow solar-pond applications at Tehran. Energy Convers Mgmt 1987;27(1):33–8. [6] Ali HM, Akhlaghi M. Experimental study in a shallow solar-pond. Solar Wind Technol 1987;4(4): 425–30. [7] Dutt DK, Rai SN, Tiwari GN. Transient analysis of a shallow solar-pond water heater integrated with a baffle plate. Energy Convers Mgmt 1987;27(3):303–7. [8] Madhuri, Tiwari GN. The effect of a baffle plate on the transient performance of a shallow solarpond’s water. Energy Convers Mgmt 1986;26(7):217–20.
S. Aboul-Enein et al. / Applied Energy 78 (2004) 159–177
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[9] Parkash J, Garg HP, Hrishikesan DS, Ranjana JHA. Performance studies of an integrated solar collector-cum-storage water-heating system with transparent insulation cover. Solar Wind Technol 1989;6(2):171–6. [10] Parkash J, Garg HP, Datta G. Performance prediction for a built-in-storage-type solar water-heater. Energy 1985;10(11):1209–13. [11] Wattmuf JH, Carter WWS, Proctor D. Solar and wind induced external coefficients for solar collectors. Comples 1977;2. [12] Swinbank WC. Long-wave radiation from clear skies. QJR Meteorol Soc 1963;89. [13] Rabl A, Nielsen CE. Solar ponds for space heating. Solar Energy 1975;17:1–12. [14] Singh AK, Tiwari GN. Thermal evaluation of regeneration active solar distillation under thermosyphon mode. Energy Convers Mgmt 1993;34:697–709. [15] Garg H.P. Treatise on solar energy, Vol. I: Fundamentals of solar energy. New York: John Wiley & Sons; 1982 [chapter 3] [16] Hollands KGT, Unny TE, Raithby GR, Konicek L. J Heat Transfer 1976;98:189–93. [17] Fishenden M, Saunders OA. An introduction to heat transfer. Oxford: University Press; 1950. [18] McAdams WH. Heat transmission. McGraw-Hill 1954. [19] Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: John Wiley & Sons; 1980 [chapter 6] [20] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. New York: John Wiley & Sons; 1991. [21] Tiwari GN, Sangeeta Suneja. Solar thermal engineering systems. London: Narosa Publishing House; 1997. [22] Wong HY. Heat transfer for engineers. New York: Longman; 1997 [chapter 3] [23] Metias MZ. Mathematical modeling of solar-concentrator systems: solar-box cooker. M. Sc thesis, Cairo University, 1992.