Heat transfer augmentation in solar thermal collectors using impinging air jets: A comprehensive review

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

Heat transfer augmentation in solar thermal collectors using impinging air jets: A comprehensive review ⁎

Ranchan Chauhana, , Tej Singhb, N.S. Thakurc, Nitin Kumara, Raj Kumara, Anil Kumard a

Faculty of Engineering and Technology, Shoolini University, Solan, HP 173229, India Department of Mechanical Engineering, Manav Bharti University, Solan, HP 173229, India c Centre for Energy and Environment Engineering, NIT Hamirpur, HP 177005, India d Energy Technology Research Centre, Department of Mechanical Engineering, Prince of Songkla University, 90110, Thailand b

A R T I C L E I N F O

A B S T R A C T

Keywords: Solar thermal collector Jet impingement Heat transfer Friction factor Multi criteria decision making

Jet impingement has led to considerable augmentation in heat transfer characteristics of solar thermal collectors. The impinging air jets are characterized by different control factors where it becomes essential to study their dependence on performance defining criteria so as to arrive at the optimized impinging jet geometry which create one or combination of following conditions favorable for heat transfer with minimal friction losses inside the collector: (a) breaking laminar sub layer (b) increasing turbulent intensity (c) increasing heat transfer area, and (d) generating vortex or secondary flows. The present article examines the thermodynamic behavior of solar thermal collector, review the experimental investigations reported in the literature to study the dependence of control factors on heat transfer and friction characteristics and review the multi criteria decision making methods towards optimization of control factor combinations for an optimal design of the impinging jet solar thermal collector. This study provides a platform for scientists working in the same research field to design a better heat transfer enhancement contrivance in the form of jet control factors to improve the thermohydraulic performance by maximizing the energy output from the system.

1. Introduction The future energy demands are increasing both on account of increase in population and standard of living in various parts of globe which has made the human minds to focus the need for alternate energy options available. Clearly, humankind has to set a different course in its need for energy, one that involves less intrusive sources such as solar, wind and geothermal energy. They are the energy sources which do not harm the planet and will never run out. It needs to be again in the crucial areas of energy and the environment in order to assure sustainability for future generations. Solar energy can be used to meet various future energy requirements and is enduring source of energy which is also environmental friendly. The solar thermal collector possesses a significant position amongst solar thermal systems ever since it is extensively used in numerous commercial applications such as to supply hot air to the buildings, industrial and agricultural drying etc. [1]. The solar thermal collectors possess low value of thermal efficiency because of lower convective coefficient of heat transfer between the heated absorber plate surface and the air which increases in the temperature of the system leading to elevated heat losses from the collector and finally lowers its thermal efficiency [2]. The heat from the absorber ⁎

plate is to be convected efficiently to the air flowing underneath it to augment its overall performance. The lower value of convective coefficient of heat transfer in general is attributed by the existence of viscous sub layer, which has to be wrecked or disturbed so that maximum heat transfer may be achieved by several methods [3]. Also, the performance improvement of solar collectors has been in progress using various other improvements experimentally and analytically [4,5]. Jet impingement over the heated absorber plate marginally improves the convective coefficient of heat transfer because of very thin boundary layer formation compared to parallel air flows [6]. Jet impingement has proved its effectiveness in number of engineering and industrial applications [7–11]. Several authors have studied the heat transfer characteristics of single/multiple jet arrays. Singh et al. [12] performed experimentations to study the flow and heat transfer characteristics of air jet impingement cooling of heated circular cylinder which was maintained at constant heat flux conditions. Luhar et al. [13] performed steady state modeling of non-uniform convective cooling using jet impingement on a microprocessor chip. In their study, the thermal performance in steady and transient conditions were modeled and helped in improving the thermal design and microprocessor optimization. Wang et al. [14] performed an experimental investigation to study the

Corresponding author. E-mail address: [email protected] (R. Chauhan).

http://dx.doi.org/10.1016/j.rser.2017.10.025 Received 29 December 2016; Received in revised form 6 July 2017; Accepted 26 October 2017 1364-0321/ © 2017 Published by Elsevier Ltd.

Please cite this article as: Chauhan, R., Renewable and Sustainable Energy Reviews (2017), http://dx.doi.org/10.1016/j.rser.2017.10.025

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Nomenclature

Ap Cp Dh En Es f FR F′ G H I L ṁ Pm (ΔP )d Qu

Tfi Tfo Tpm Tfm Tsun Ta UL V W

Area of absorber plate, m2 Specific heat of air, J/kg K Hydraulic diameter of the rectangular duct, m Net exergy flow, W Exergy inflow associated with solar irradiation collector, W Friction factor Collector heat removal factor Collector efficiency factor Mass velocity of air, kg/m2 s Height of the rectangular duct, m Solar radiation intensity, W/m2 Length of test section, m Mass flow rate, kg/s Pumping power, W Pressure difference across the test section, N/m2 Rate of useful energy gain by solar collector, W

Temperature of inlet fluid, K Temperature of outlet fluid, K Mean plate temperature, K Mean fluid temperature, K Temperature of sun, K Ambient air temperature, K Overall heat loss coefficient Velocity of air in the duct, m/s Width of the rectangular duct, m

Greek symbols

ρa ηeff ηexr ηeff ηc τα

effect of vortex generators on heat transfer placed in the cross flow channel upstream of the jet exit. Bu et al. [15] studied jet impingement heat transfer for aircraft wing anti-icing application using Piccolo tube having aligned jet holes. The parametric effects of impingement heat transfer were revealed in the study and determined optimum tube to surface distance. Hosain et al. [16] studied the heat transfer by turbulent water jets impinging on hot flat steel plates at temperature lower than the boiling point so as to understand the convective heat transfer phenomenon. Aboghrara et al. [17] performed experimental investigation to study the dependence of geometrical parameters on efficiency of jet impingement onto the corrugated heat absorbing surface. They reported 14% more efficiency than conventional design at mass flow rate of 0.01–0.03 kg/s. Huang et al. [18] studied the effect of Reynolds number varied between 800 and 1700 of mixture of air/butane and the distance between nozzle and plate on heating performance of the flame. Craft et al. [19] modeled flow and heat transfer from a row of round jets impinging onto a concave semicircular surface to reproduce important flow features found in internal turbine blade cooling applications. Hasan et al. [20] carried out experimental investigation of jet array impingement using nano-fluids on the photovoltaic thermal collector which resulted in higher electrical and thermal performances. In the entire above research studies the objectives have been concerted in investigating the characteristics of heat transfer and friction behavior related to the particular application. The enhancement in heat transfer is accompanied by generous increase in frictional losses inside the fluid flow channel [21] and both of these factors depend upon the geometric configuration and operating flow Reynolds number. Several investigations have been carried out by the researchers and scientists using impinging air jets in solar thermal collectors and thus, there is need to review the past and current research so that the further research scopes can be identified and implemented. The present article is thus aimed with following objectives:

Density of air, kg/m3 Effective efficiency Exergetic efficiency Thermal efficiency Carnot efficiency Transmittance absorptance product

batch wise for each objective clearly addressed and explained in their respective context. Firstly, the thermodynamic framework has been performed based upon the first and the second law of thermodynamics, in terms of effective and exergy efficiency respectively. Secondly, the heat transfer distribution and friction behavior of the impinging air jets in a solar thermal fluid flow passage have been reviewed; above and beyond the heat transfer augmentation methods by variation in the control factors of the impinging jets are presented. Thirdly, the multi criteria decision making methods for optimization of control factor combinations have been procedurally explained in detail so as to provide the fellow researchers with all the valuable information at one place. Lastly, the scope for further research has been discussed so as to maximize effective energy delivery while minimizing the friction losses inside the collector channel.

2. Solar thermal collector Solar thermal collector is a kind of heat exchanger that transforms solar radiation energy into internal energy of the transport medium. The schematic diagram of conventional solar thermal collector is as shown in Fig. 1.

(a) To carry out thermodynamic modeling of solar thermal collector based upon effective and exergy efficiency criterion. (b) To study the augmentation in heat transfer and fluid friction using impinging air jets in solar thermal collector passage. (c) To study the potency of multi criteria decision making methodologies for successful implementation in solar thermal collectors. (d) To discuss the scope for further research in solar thermal air collectors using impinging air jets towards maximizing energy efficiency. In order to achieve the desired objectives, the article is structured

Fig. 1. Schematic diagram of conventional solar thermal collector [22].

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3.2. Exergy efficiency criterion

The absorber surface of conventional solar thermal collector is made up of aluminum due to its high thermal conductivity and is blackened in order to absorb maximum incoming solar radiations and transforms this thermal energy to the air flowing beneath [23]. The back side of the air collector is insulated so as to prevent back thermal loss from the system. Also, the sides of the solar thermal collector are well insulated so that the heat losses may be minimized to the maximum possible level. The solar thermal collector is covered with glass cover on top so that maximum incoming solar radiations may get trapped inside and heats the absorbing surface. The ambient air enters the solar thermal collector duct from one side, gets heated up as it comes in contact with the heat transferring absorber plate through convection mode of heat transfer and exits from the other side. The heated air can be used for various purposes to meet daily domestic and industrial energy requirements [24].

Exergy analysis is an assessment technique for systems and processes based on the second law of thermodynamics and can be defined as the maximum work potential which can be obtained from a form of energy [34]. The exergy analysis yields useful results as it deals with irreversibility minimization or maximum exergy delivery [35]. The exergy flow diagram of solar thermal collector is as shown in Fig. 4. Altfeld et al. [36] proposed a method based upon second law of thermodynamics for establishing the equivalence of useful energy and frictional losses. The exergetic efficiency of solar thermal collector is expressed as:

ηexr = En/ Es

where, the net exergy flow (En ) is the increase in exergy flow of air while flowing through the collector and is to be maximized for optimization. The exergy flow can be expressed as:

3. The thermodynamic framework

En = IAp ηth ηc − Pm (1 − ηc ); Where ηc = 1 − Ta/Tfm

The effectiveness of the system under study is important to investigate so that the technical advancements may further be carried out with a view to accelerate the energy output from the system. The performance of solar thermal collector can be evaluated based upon first and second law of thermodynamics in terms of effective and exergy efficiency criterion respectively. These are discussed in following sub sections.

Also, the exergy inflow associated with solar irradiation (Es ) is given

Es = I × Ap (1 − Ta/ Tsun )

4. Impinging jet solar thermal collector

(1)

Thermal performance of a solar air collector has been found to be poor on account of its low thermal capacity. Thermal performance of a

where, FR is the correction factor, also known as collector heat removal factor, obtained as [26]:

̇ p ⎛ mC UL F ′Ap ⎤ ⎞ 1 − exp ⎡ ⎟ ⎢ mC ̇ p ⎥ Ap UL ⎜ ⎣ ⎦⎠ ⎝

(2)

In Eq. (2) F ′ is the collector efficiency factor which decreases with increase in overall loss coefficient. The overall heat loss coefficient (UL) is the heat transfer resistance from the absorber plate to the ambient air and was developed by Klein [27] following the basic procedure of Hottel and Woertz [28]: Finally, the collector's thermal efficiency is obtained as follows [29]:

ηth = FR ⎡ (τα ) − UL ⎛ ⎢ ⎝ ⎣

⎜

Tfi − Ta ⎤ ⎞ I ⎠⎥ ⎦ ⎟

(3)

The effective efficiency is evaluated on the basis of net thermal energy gain as [31]:

ηeff =

Qu − Pm/ C I × Ap

(4)

where, (Pm) is the mechanical power required to propel the air through the solar thermal collector duct [32]. The effective efficiency finally attains the form [33]:

ηeff = ηth −

fLV 3ρa (W + H ) C × Ap × I

(8)

The exergetic efficiency of the system can be maximized by maximizing (En ) which can be done by minimizing the exergy losses taking place in the collector. The variation in thermal efficiency and exergetic efficiency of solar thermal collector is as shown in Fig. 5. It can be seen that the exergetic efficiency first increases at lower values of Reynolds number, attains maxima and decreases thereafter due to increase in exergy losses. Apart from exergy losses due to absorption, the exergy losses due to internal irreversibilities i.e. heat transfer from the absorber to the fluid at finite temperature difference and friction in the fluid flow duct [37] affects the exergetic efficiency of the solar collector.

The effective efficiency criterion takes into account both the thermal as well as hydraulic components for performance evaluation. The energy flow diagram is as shown in Fig. 2. Under steady state conditions, the useful heat delivered by the collector is equal to the energy absorbed by the carrier fluid minus direct and indirect heat losses from collector to the surroundings. The useful energy collected from the solar thermal collector can be obtained as [25]:

FR =

(7)

by:

3.1. Effective efficiency criterion

Qu = Ap FR [I (τα ) − UL (Tfi − Ta)]

(6)

(5)

The variation in thermal and effective efficiency of conventional solar thermal collector is as shown in Fig. 3.

Fig. 2. Energy flow diagram of solar thermal collector [30].

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0.12 Thermal efficiency Exergetic efficiency

0.6

0.11

Thermal efficiency, η th

0.10 0.4 0.09 0.3 0.08 0.2

Exergetic efficiency, η exr x 10

0.5

0.07 0.1

Fig. 3. Variation of thermal and effective efficiency of conventional solar thermal collector with Reynolds number.

2000

4000

6000

8000

10000

Reynolds Number, Re Fig. 5. Exergetic and thermal efficiency as a function of Reynolds number.

solar air collector depends upon different parameters such as incident solar radiations, losses from the absorber plate and convective heat transfer coefficient between air and the absorber plate. Broadly, the performance enhancement of solar thermal collectors may be carried out by: Enhancement of intensity of incident solar radiation on the collector; Reduction of thermal losses from the collector; Flow passage modifications for enhancement of convective heat transfer coefficient. Enhancement in the intensity of solar radiations on the absorber surface of solar collector with the help of reflectors increases the performance of solar collector by increasing the total collection area [38,39]. The reduction in thermal losses from the collector can also enhance the performance of solar air collector by using two or more glass covers and by using selective surfaces [40]. Further, modifications in the air flow channel help in enhancing the convective heat transfer coefficient and thereby the overall performance of the solar collector is

augmented. Modifications can be in the form of packed bed [41–43], use of extended surfaces [44,45], use of artificial roughness [46,47] or by jet air impingement over the surface heated by solar radiations. Jet impingement over the heated surface transfers about three times of thermal energy as compared to the conventional method [48]. The schematic diagram of impinging jet solar thermal collector is as shown in Fig. 6. The jets of air impinging on the absorber plate, which is the heat transferring surface, helps in increasing heat transfer coefficient and thereby increasing the rate of heat transfer. An array of jets provided on the jet plate impinges normally on to the absorber plate and exits from the other side. Studies have reported that impinging jets released against the heat transferring surface can efficiently transfer large amount of thermal energy and mass between the surface and the Fig. 4. Exergy flow diagram of solar thermal collector [36].

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generated by the shear between wall jet and surrounding fluid which is transported to the boundary layer at the heat transfer surface. Compared with conventional convection cooling by confined flow parallel to (under) the cooled surface, jet impingement produces heat transfer coefficients that are up to 3 times higher because the impingement boundary layers are much thinner as shown in Fig. 8 and often the spent fluid after impingement serves to turbulate the surrounding fluid. Also the flow required from an impinging jet device for a required heat transfer coefficient may be two orders of magnitude smaller than that required for a cooling approach using free wall parallel flow [55].

Fig. 6. Impinging jet solar thermal collector [33].

5.1. Heat transfer distribution

fluid. Compared to other heat and mass transfer arrangements that do not employ phase change, jet impingement offers efficient use of fluid, and high transfer rates [49]. Rajaseenivasan et al. [50] carried out experimentation over the impinging air jets in a solar thermal collector to study the thermal performance with varying angle of attack. Nayak and Singh [51] studied the effect of geometrical aspects of jet plate solar air collector with varying parameters such as mass flow rate varied from 0.030 to 0.065 kg/s and 0.20 to 0.043 kg/s; Reynolds number varied from 2700 to 6900; depth ratio varied from 0.75 to 1.0. In their study the performance of impinging jet solar thermal collector delivered higher efficiency compared to the conventional solar thermal collector. The Nusselt number and friction factor correlations were also developed by the authors. Zukowski [52] investigated the thermal and fluid flow characteristics of a novel microjet air solar collector and reported efficiency of energy conversion in the range 60–90%. Chauhan and Thakur [53] developed heat transfer and friction factor correlations for impinging jet solar air collector with different flow and geometric variations. In their study, the experimentation encompassed the reynolds number range of 3800–16,000; jet diameter ratio of 0.043–0.109; streamwise pitch ratio of 0.435–1.739 and spanwise pitch ratio of 0.435–0.869.

Heat transfer distribution to the impinging air jet has been studied by several investigators on both flat and curved surfaces by single jet, line of jets and an array of jets. Heat transfer beneath a single axisymmetric jet has been studied by Ichimiya [56] for both normal and oblique impingement angles to determine the angling effects of jet impingement. A similar study for confined jets was carried by Lin et al. [57] using two dimensional, normal jets and varying target spacing. The studies reported enhancement in heat transfer coefficient from the heated surface. Heat transfer has been explored by using single line of impinging jets. Heat transfer distribution due to line jet impingement with and without film extraction effects was carried out by Metzer and Bunker [58]. This class of impingement with crossflow effects in a channel was extended by Metzer and Korstad [59]. The relative strengths of the jet flow and crossflow have been reported to be important in determining the heat transfer. For heat transfer from large surfaces, array of impinging jets are used. Several studies have been carried out to correlate the jet impingement heat transfer under an array of impinging circular jets. Lam and Prakash [60] carried out numerical investigation and design optimization of impingement cooling system with an array of air jets and reported heat transfer and entropy generation. Pareto optimal solution sets were also determined using multi objective genetic algorithm. The heat transfer distribution from an array of impinging tangential jets in a triangular duct was studied by Huang and Chang [61]. For the study, three types of outflow orientations were considered to measure the detailed heat transfer coefficient and recommended that the triangular duct with two openings for highest wall averaged heat transfer and moderate loss coefficient. Also, correlations for wall averaged heat transfer, Nusselt number and loss coefficient in a triangular duct were developed by the authors. Fu et al. [62] reported surface heat transfer study of ultra heavy plate during quenching process using jet array impingement and developed multi channel temperature tracking recorder. Florschuetz et al. [63] studied heat transfer characteristics of impinging jets with cross flow. The impingement plate consisted of an array of rectangular electrical plate heaters arranged in stream-wise direction and the heaters were so

5. Hydrodynamics of impinging jets Typically the jet is turbulent at the nozzle exit and is characterized by a uniform velocity profile. However with increasing distance from the exit, momentum exchange between the jet and the ambient causes the free boundary of the jet to broaden and the potential core, within the uniform exit velocity is retained to contract. Downstream of the potential core the velocity profile is non uniform over the entire jet cross section and the maximum (centre) velocity decreases with increasing distance from the nozzle exit [54]. The region of the flow over which conditions are unaffected by the impingement (target) surface is termed the free jet. It is illustrated in Fig. 7 for single jet impingement. Within the stagnation or impingement zone, flow is influenced by the target surface and is decelerated and accelerated in the normal (z) and transverse (x) directions respectively. However since the flow continues to entire zero momentum fluid from the ambient, transverse acceleration cannot continue indefinitely and accelerating flow in the stagnation zone is transformed to decelerating in the wall jet. Hence with increasing x, the velocity components parallel to the surface increases from a value of zero to some maximum and subsequently decay to zero. Velocity profiles within the wall jet are characterized by zero velocity at both the impingement and free surfaces and thus convection heat and/or mass transfer occur in both the stagnation and wall jet regions. For multiple jet impingements the flow field is influenced by two types of interactions which do not occur in the case of single jets. The flow pattern of multiple jet impingements can be divided into six characteristics regions: free jet region; impinging region; wall jet region; fountain formulation region; fountain upwash region; entrainment. The fountain formulation zone is formed as a result of interference of wall jets of the neighboring jets. The wall jet region exhibits higher heat transfer than that of parallel flow due to turbulence

Fig. 7. Surface impingement of a single round or slot gas jet [21].

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Fig. 8. Comparison between boundary layer of jet impingement and parallel flow [55].

Numerical computations were carried out for two types of arrangements, inline and staggered and three different orientations, parallel, hybrid and counter for Reynolds number in range 2440–14,640 and jet to plate spacing of 1, 3 and 6. In all the above considered cases the highest average Nusselt number was obtained for inline jets and hybrid cross flow orientation. The thermal performance of multiple impinging round jets is enhanced when the jet to target spacing decreases from 6 to 3. The role of jet inlet geometry and aspect ratio on local and average heat transfer characteristics of impinging jets were investigated experimentally and numerically by Koseoglu and Baskaya [73]. Three exit geometries viz. circular, elliptic and rectangular were considered in the study with different aspect ratios. Heat transfer enhancement was obtained in elliptic and rectangular geometry as aspect ratio of equal cross-sectional area increases at same jet to plate distance of 2 and 6. Chaudhari et al. [74] studied the effect of shape of orifice of synthetic jet assembly of impingement cooling on heated surface with square, circular and rectangular orifice of different aspect ratios at Reynolds number range of 950–4000. Jet impingement with square orifice nozzle provided maximum enhancement in heat transfer than rectangular and circular orifice at large axial distances. At small axial distances and same hydraulic diameter, rectangular orifice performed better than other geometries. It was concluded that a rectangular orifice with larger hydraulic diameter and smaller aspect ratio is the best option for space constrained systems as far as impingement cooling of heated surface is concerned. Jet impingement in solar thermal collector involves low range of Reynolds number and most appropriate studies applicable for such collectors were those carried out by Kercher and Tabakoff [75], Kuroda and Nishioka [76]. Kercher and Tabakoff [75] conducted similar experiments and concluded that as the total hole area to total heat transfer area increases, the heat transfer coefficient also increases. The heat transfer performance is increased by decreasing diameter of holes with increasing number of holes keeping everything else equal. Heat transfer was dominated by diameter of holes, Reynolds number and the holes spacing to holes diameter ratio. Choudhury and Garg [77] modeled the jet impingement process for average heat transfer coefficient over the heat transfer surface which is the function of jet Reynolds number, fluid flowing through the duct and the duct dimensions. It was concluded that with the same separation distance between the absorber and the back plate in both the collector types, even with cross flow and with holes on the jet plate, the performance efficiency of jet concept thermal collector was significantly higher than that of the parallel plate air collector which establish the superiority of the jet plate air collector for variety of solar thermal applications. Performance of jet impingement in solar air collectors has been studied by Belusko et al. [78] and found increase in thermal efficiency of about 21% to that of conventional solar air collector. He reported that increase in pitch between the jets results in increase in heat transfer and higher heat transfer rated can be obtained with higher spacing but the pumping power has to be taken into account.

adjusted to give proper amount of power in order to keep the temperature of the plate constant. Correlation for Nusselt Number for both inline and staggered arrangement were presented based on the experiments conducted by the authors. Heat transfer characteristics for inline and staggered arrays of circular jets with cross-flow of spent air were studied by Metzger et al. [64]. Ten rows of impinging jets were experimentally studied and found that local nusselt number varies periodically for first ten rows with nusselt number highest in line with the holes and the lowest halfway between two holes. More recently Gao et al. [65] used the correlations available in the literature on an linearly stretched arrays and found that the correlations matched fairly well. The heat transfer distribution from a linearly stretched array on the heat transferring surface was determined and found enhanced values of heat transfer coefficient at all values of Reynolds number. Ingole and Sundaram [66] experimentally investigated heat transfer characteristics of inclined jet at Reynolds number 2000–20,000. Authors also developed equations for average Nusselt number for inclined nonconfined air jet for cooling applications. Dyban et al. [67] carried out experimental investigation for local heat transfer at the surface blown by an array of round impinging jets with the spent air exhaust on one side. The collector relationships obtained for the range of parameters considered were used for calculation of the air flow rate distribution over the length of perforation of the jet flow and stalling flow velocity ratio and of the total hydraulic resistance coefficient for the jet arrays considered. Also a relationship was obtained for optimum value of open perforated surface and distance expressed in fractions of the entire heat transfer surface length. An experimental investigation was carried out by Baydar [68] for the flow field between two horizontal surfaces arising from a jet issuing from the lower surface and impinging normally on the upper surface for the Reynolds number range of 300–10,000; nozzle to plate spacing ranges 0.5–4. The effect of Re and nozzle to plate spacing was investigated. It was found that the characteristics of an impinging circular jet in a confined region were sensitive to nozzle to plate spacing. A comparative study of five Reynolds number k-epsilon models for impingement heat transfer was carried out by Wang and Mujumdar [69] for the prediction of heat transfer under two dimensional turbulent slot jet and compared with available experimental data. It was concluded that the jet inlet velocity profile that provide slow jet spreading rate increases the heat transfer in and near the impinging regions until a critical value of X/W is reached. Dagtekin and Oztop [70] carried out numerical investigation for heat transfer due to double impinging vertical slot jets onto an isothermal wall for laminar flow regime and the effect of jet Reynolds number, the jet isothermal bottom wall spacing and distance between two jets on heat transfer and flow field was examined. Sivasamy et al. [71] simulated numerically the two dimensional laminar incompressible impinging slot jet to gain insight into flow characteristics. The behavior of the impinging jet was discussed in detail with respect to aspect ratio and Reynolds number. Based upon the study a correlation for the reattachment length was proposed for the Reynolds number range of 100–500. Miao et al. [72] investigated the fluid flow and heat transfer characteristics of round impinging jet arrays impinging orthogonally on the flat plate with confined walls at different cross-flow orientations. 6

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They concluded that the flow rate and solid material properties influence the convective heat transfer. Jet impingement heat transfer on the surface with dimples was investigated by Kanokjaruvijit and Martinez [88] and an enhancement of about 50% have been reported by the authors depending upon the crossflow condition and distance between the jets and impingement surface. Craft et al. [89] modeled flow and heat transfer from a row of round jets impinging onto a concave semicircular surface to reproduce important flow features found in internal turbine blade cooling applications. Ekkad and Kontrovitz [90] presented a detailed heat transfer distribution over a jet impingement target surface with dimples. The effect of dimple pattern and dimple depth on the heat transfer distribution was also investigated for Reynolds number range of 4800–14,800. It was concluded that the presence of dimples on the target surface produced lower heat transfer coefficients than the plate without dimples. Katti and Prabhu [91] carried out experimental investigation to study the heat transfer enhancement on a flat surface with axisymmetric detached rib roughners due to normal impingement of circular air jet and the effect of rib width, rib height, pitch between the ribs, location of first rib from the stagnation point and clearance under the rib on the local heat transfer distribution were studied. The ratio of average nusselt numbers of ribbed and smooth surface increased with increase in Reynolds number.

5.2. Heat transfer augmentation methods Several methods have been employed with a view to enhancing the overall heat transfer to an impinging jet flow. Some of these methods are discussed below: 5.2.1. Nozzle geometry Nozzle geometry is believed to have significant effect in overall heat transfer from heated surface to impinging air jet and has attracted much research in recent years. The shape and size of the nozzle for efficient heat transfer has been a question for investigators. The effect of nozzle inlet chamfering with a view to enhance heat transfer was studied by Brignoi and Garimella [79]. It was concluded that while the inlet chamfering angle had a large effect on pressure drop across the nozzle, the effect of heat transfer coefficient was not significant. Lee and Lee [80] investigated the effect of jet exit chamfering on heat transfer to impinging air jet. The chamfering on the exit of the jet showed more expansion of jet than the sharp edged orifice. Enhancement of about 25–55% has been reported for fully developed pipe jet and 50–70% for countered nozzle. Whelan and Robinson [81] investigated the nozzle geometry effects in liquid jet array impingement for Reynolds number ranging 800–10,000, nozzle to jet target spacing of 20 mm. Attala and Salem [82] carried out experimental investigation to study the effect of nozzle geometry on heat transfer characteristics. Based upon the study it was reported that the highest value of Nusselt number was observed for square edge inlet nozzle compared to that of other nozzle configurations. Liu and Feng [83] carried out numerical investigation to study the effect of jet nozzle position on impingement cooling of gas turbine blade leading edge. The investigation concluded that the area averaged Nusselt number increase with increase in Mach number and increases with decrease in distance between the jets. Also the correlations for area weighed Nusselt number were derived for the range of parameters investigated.

5.2.4. Turbulence promoters Turbulence promoters used for creating turbulence in the jet flow can enhance heat transfer to the impinging air jets. Zhou and Lee [92] studied the effect of heat transfer by installing mesh screens across the nozzle exit with various mesh solidity which increases turbulence in the stagnation zone. The presence of mesh screen across the nozzle exit helps in increasing turbulence in the stagnation zone and thus increases heat transfer through the impingement surface. 5.3. Discrete optimization approaches

5.2.2. Jet to jet spacing Jet to jet spacing in an array of impinging jets can help in increasing heat transfer coefficients by decreasing interference between the jets. Various researches have been carried out to study the jet to jet spacing in view of enhancing heat transfer. Effect of hole spacing on spatially resolved heat transfer from an array of jets impinging on a flat plate was studied by Goodro et al. [84] for a Reynolds number range of 8200–30,500. The spacing of holes considered in the experiments was 8 or 12 times that of jet diameter in both spanwise and streamwise directions. Dependence of heat transfer enhancement on Mach number was investigated and concluded that heat transfer increased as the Mach number increases for both the jet spacings. Katti and Prabhu [85] carried out experimental investigations to study the heat transfer distribution with varying jet to jet spacing on the jet plate. The effect of spanwise pitch spacing of inline array of impinging jet was studied for length to diameter ratio of nozzles on the jet plate of 1.0. Based upon the results of the investigation a simple correlation to predict the streamwise distribution of heat transfer coefficient averaged over each spanwise strip resolved to one jet hole was developed by the authors. Huber and Viskanta [86] studied the effect of jet to jet spacing on convective heat transfer to confined, impinging jet arrays of axisymmetric air jets for 3 different values nozzle to plate spacing for Reynolds number ranging 3500–20,400. It was concluded that the jet to jet spacing affects the convective heat transfer coefficient from the heated plate to the flowing fluid.

Problems encountered in real world constitute more than one criterion for which the multi criteria decision making approaches have been developed to solve such complex tribulations. The MCDM evaluates the overall preference among the existing alternative sets or options which is the closest to the ideal solution and farthest to the worst. Chauhan et al. [93] used a preference selection index (PSI) method for evaluating a best alternative set for parametric selection in solar thermal collectors provided with impinging air jets. They evaluated in total 18 alternative sets and optimized the best alternative combination using PSI method. Chamoli [94] used the same methodology for optimizing parameters in solar collectors with V down baffles as turbulence promoters. Chamoli [95] also studied the hybrid fuzzy analytic hierarchy process (AHP) and technique for order of preference by similarity to ideal solution (TOPSIS) methodology for optimizing V down baffle parameters in a solar thermal fluid flow passage. Sharma et al. [96] optimized the baffle parameters using multi criteria decision making in which weight determination was carried out using entropy method. Beltran et al. [97] applied analytical hierarchy process and analytical network process to help the managing board of Spanish solar power company to manage and determine the order of priority of the project investment in the company portfolio. Nixon et al. [98] carried out design analysis of solar thermal collector for industrial application using multi criteria decision making methodology. Cavallaro [99] in his study proposed and validated the effectiveness of TOPSIS fuzzy method by comparing different heat transfer fluids in a solar thermal storage system. All these multi criteria decision making methods have validated their effectiveness in a number of solar thermal energy systems. The procedural detail of each of the MCDM methods in discussed which consists of three basic stages: Identification of the alternatives and criterions; Criterion weight calculation; Selection of best alternative as shown in Fig. 9.

5.2.3. Surface finish The surface finish of the heat transferring surface is another parameter for enhancement of heat transfer to an impinging air jet. Dobbertean and Rahman [87] carried out numerical analysis of steady state heat transfer characteristics of impinging air jets on patterned surfaces to study the effect of rectangular steps and triangular ribs. 7

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5.3.2.2. Entropy method. First of all the entropy for each criterion is calculated as: n

dij

Εj = −ƛ ∑

m

∑i = 1 dij

j=1

ln(

dij m

∑i = 1 dij

) Where ƛ =

1 is a constant ln(m) (12)

Finally, the weight of each criterion is calculated as:

ωj =

n

1 − Εj n ∑ j=1 1

ωj ≥ 0 and

− Εj

∑ ωj = 1 (13)

j=1

5.3.3. Stage 3: selection of best alternative In this stage, ranking of the alternatives are determined by using TOPSIS, VIKOR, GRA and PSI methods. 5.3.3.1. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. The TOPSIS method was developed by Hwang and Yoon [103] where the best alternative has the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution [104,105]. Generally, the TOPSIS method is composed of following steps: Step I: The decision matrix is normalized as: Fig. 9. Flowchart for computation of optimized combination of control factors.

Dij =

5.3.1. Stage 1: identification of the alternatives and criterions In stage 1 alternatives and criterions used for the assessment of given problem are identified. Thereafter a decision matrix which shows assessments of various alternatives according to criterions is created as: C1

A1 ⎡ d11 A2 ⎢ d21 ⎢ ⋮ ⎢ ⋮ d= Ai ⎢ di1 ⋮ ⎢ ⋮ ⎢ Am ⎢ dm1 ⎣

C2

d11 d22 ⋮ di2 ⋮ dm2

⋯

Cj

⋯ ⋯ ⋮ ⋯ ⋮ ⋯

⋯

d1j d2j ⋮ dij ⋮ dmj

d1n ⎤ d2n ⎥ ⎥ ⋮ ⎥ din ⎥ ⎥ ⋮ ⎥ dmn ⎥ ⎦

ℏ+ = (ωD1+, ωD2+.... ωDn+) = {Max wDij | j ∈ P, Min wDij | j ∈ L} ℏ− = (ωD1−, ωD2−.... ωDn−) = {Min wDij | j ∈ P , Max wDij | j ∈ L}

(9)

(16) where, P is related with the benefit criterion and L is related with the loss criterion. Step IV: The Euclidian distances are calculated as: n

αi+ =

cnn

⋯

ωi =

n ∑i = 1

⎧∏n ⎨ j=1

ψi =

⎩

Aij ⎫ ⎬ ⎭

for i

j=1

(17)

αi+

αi− + αi−

for i = 1, 2, ... ,m

(18)

Finally, the alternatives are arranged in descending order of their closeness coefficient. The alternative which tops the list is the most preferred one. 5.3.3.2. Vise Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) approach. VIKOR also known as compromise ranking method was mainly established by Zeleny [106]. The method focuses on selecting and ranking the set of alternatives and a compromise solution is obtained with the initial weights of a problem with conflicting criterion [96,101]. The various steps for the VIKOR methods are listed as follows: Step-I: After the development of decision matrix, values of profit (dij )max and loss (dij )min criterion is obtained as:

(10)

1 n

1 n

∑ (ωDij − ωD−j )2

Step V: The closeness coefficient (ψi ) value of the alternatives is calculated as:

Thereafter, relative weight (ωi ) of each criterion is determined as:

⎧∏n C ⎫ j = 1 ij ⎬ ⎨ ⎭ ⎩

αi− =

= 1, 2, ... ,m

Cn

⋯ C1n ⎤ 1 ⋯ C2n ⎥ Cii = 1, Cji = , Cij ≠ 0 ⋱ ⋮ ⎥ Cij ⎥ ⋯ Cnn ⎦

n

∑ (ωD+j − ωDij)2 , j=1

5.3.2.1. Analytical Hierarchy Process Method (AHP) method. AHP is a structured technique proposed by Saaty [100]. In AHP, the relative importance of each criterion is determined by using a pair-wise comparison matrix in accordance to Saaty's nine-point scale [100–102]. For n criterion the comparison matrix (C) is given as: C2

(15)

Here, ωj is the weight of the jth criterion as determined with AHP or Entropy method. Step III: The positive ideal solution (ℏ+) and the negative ideal solution (ℏ−) are determined from the ωDij as shown:

5.3.2. Stage 2: criterion weight calculation In stage 2, the criterions used in the assessment of a given problem are assigned with weights. Generally, AHP and entropy method are employed for weight determination.

C1

(14)

ωDij = Dij × ωj

where, Ai (i = 1, 2, …, m) is the ith alternative; Cj (j = 1, 2, …, n) is the jth criterion and element dij represents the performance of alternative Ai with respect to criterion Cj .

C1 ⎡ C11 C12 C2 ⎢ C21 C22 = ⋮⎢ ⋮ ⋮ ⎢ Cn ⎣Cn1 Cn2

1/2

Step II: After normalization, weighted normalized matrix (ωDij ) is determined as:

Cn

⋯ ⋯ ⋮ ⋯ ⋮ ⋯

dij m

[∑i = 1 (dij2)]

i = 1, 2, …, n (11) 8

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(dij )max = max[dij , i = 1, 2... m], (dij )min = min[dij , i = 1, 2... m]

following steps: Step I: The decision matrix is as:

(19) Step II: In this step, utility (ℏi) and regret (ƛi ) measurement values are calculated as: n

ℏi =

∑ j=1 n

∑

ℏi =

j=1

ωj [(dij )max − dij] [(dij )max − (dij )min] ωj [dij − (dij )min] [(dij )max − (dij )min]

Larger the better, Dij = Smaller the better, Dij =

, if j is benefit criterion

2… ...n

ηj = (20)

πi =

A review on heat transfer enhancement in solar thermal collectors has been reported with jets of air impinging normally over the heat transferring absorber plate. Investigations have been carried out by the researchers around the globe to study the heat transfer and friction characteristics of impinging jet solar thermal collectors analytically and experimentally. It has been concluded by each research study that the thermal performance has been augmented with the use of the impinging jets compared to the parallel air flow under the absorber plate. However, the augmentation in friction factor has also been reported along with simultaneous augment in heat transfer. Effective impinging air jet geometry results in reduction of size of solar collector when the heat exchange rate is kept constant and if the size is kept constant it assist in heat extraction from the heated absorber surface exposed to sunlight. A review on heat transfer studies in solar thermal collector with different modes of efficiency augmentation techniques including packed beds, extended and V-corrugated surfaces, artificial roughness and jet impingement indicates that sufficient research work has been carried out on air collector with fins, packed bed, artificial roughness with improve in thermal efficiency in comparison to the smooth duct. The literature study also reveals that there is substantial rise in heat transfer coefficient with jet impingement and hence, improved thermal efficiency of the system. Theoretical and experimental studies indicates that solar collector with jets of air impinging over the absorber plate is more efficient than the conventional air collector for the desired range of parameters. Apart from experimental investigations, the numerical investigation with jet impingement for different applications also reveals a substantial increase in the efficiency and found suitable in many industrial applications such as cooling of turbines, cooling of a grinding process, electronic equipments etc. Although many studies have been carried with impinging air jets for augmentation in heat transfer, there are few experimental investigations which prove its superiority in solar thermal applications. Also, very few research studies over its efficient design suggests that the futuristic research initiatives should have to be performed so that its importance be investigated and an energy efficient design of solar thermal collector system be designed and commercialized. Various multi criteria decision methods have been studied by various

(23)

(24)

(25)

where, μ ∈ [0, 1] is known as the distinguishing coefficient and generally takes the value 0.5 as it offers good stability with moderate distinguishing effects. Step IV: In this step, grey correlation degree is calculated as: n

∑ [Φij] j=1

(30)

6. Discussion

minim= 1 minin= 1∇ij + μ max im= 1 max in= 1∇ij

1 n

(29)

∑ (Dij × Ψj) j=1

Step III: In this step, grey relation coefficient is determined as:

Ωi =

m

Finally, the alternatives are ranked according to the πi value and the one having highest πi value is ranked first.

max{dij} − dij

∇ij + μ max im= 1 max in= 1∇ij

N

∑ j = 1 [1 − ∑i = 1 [Dij − ηj ]2 ]

n

(22)

Step II: In this step, a difference matrix is constructed as:

Φij =

1 − ∑i = 1 [Dij − ηj ]2

Step IV: In the next step, the preference selection index (πi ) value for each alternative is determined by using the following equation:

dij − min{dij}

∇ij = max im= 1{Dij} − Dij

(28)

i=1

m

Ψj =

max{dij} − min{dij} max{dij} − min{dij}

∑ Dij

as:

5.3.3.3. Grey Relation Analysis (GRA) method. Grey relation analysis (GRA) method was proposed by Deng [107]. It is simple and straight forward MCDM method and is used to evaluate the pristine data directly without any additional interactions during the process [108]. The GRA methodology consists of following steps: Step I: The decision matrix is normalized in the range of [0, 1] according to the benefit (larger the better) and loss (smaller the better) criteria as:

Smaller the better, Dij =

(27)

m

1 m

(21)

+ + where, ℏ+i , ℏ− i , ƛi and ƛi are the maximum and minimum values of utility and regret measurements. χ is introduced as weight for the maximum value of utility and (1 − χ ) is the weight of the individual regret and normally the value of χ is taken as 0.5 [101]. Step IV: According to the value of VIKOR index, the alternatives are arranged in the ascending order and the best alternative is the one having the minimum value of VIKOR index.

Larger the better, Dij =

dij

Step III: In this step, the overall preference value (Ψj ) is determined

where, ωj is the weight of the jth criterion and determined with AHP or entropy method. Step III: In this step the VIKOR index (Ωi ) is calculated as:

(ℏi − ℏ−i ) ⎞ (ƛi − ƛi−) ⎞ αi = χ ⎛⎜ + + (1 − χ ) ⎛⎜ + − ⎟ − ⎟ ( (ℏ − ℏ ) i ⎠ ⎝ i ⎝ ƛi − ƛi ) ⎠

min{dij}

Step II: In this step, the mean of the normalized (ηj ) value is calculated as:

, if j is loss criterion, for j = 1,

ωj [(dij )max − dij] ⎫ , for j = 1, 2 … ...n ƛi = Max n of ⎧ ⎨ [(dij )max − (dij )min] ⎬ ⎭ ⎩

dij max{dij}

(26)

The alternative with highest degree of correlation will be identified as the best. 5.3.3.4. Preference Selection Index (PSI) method. Maniya and Bhatt [109] proposed PSI method for material selection process. The PSI method is intended to provide a complete ranking of the alternatives from the best to the worst [110]. The PSI methodology described in 9

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form to the other. Therefore, multi criteria decision making methods which examine the set of alternatives and suggests a useful alternative ranking from best to the worst should be applied so as an optimal design combination of control factors can be suggested for the designers and its potential users. (7) The thermodynamic modeling of solar thermal collector determines the quality of useful energy extracted as a result of input solar energy. The performance of solar thermal collector should be evaluated considering the effective as well as exergy efficiency criterion so as to determine the optimum design of the system for any particular application. Since, application of solar collectors varies from industry to industry due to variation in desired temperature range, the modifications inside the collector passage can be evaluated accordingly keeping in view the energy expenditure and desired output.

researchers and have successfully presented useful results for providing optimized results with respect to specific application. However, such MCDM approaches for implementation in solar thermal collectors lacks in majority which are not only economically efficient but also confirms about effective energy utilization. Henceforth, the experimental investigations over impinging air jets with further modifications in an air passage of solar thermal collector and an appropriate MCDM approach may lead this very branch of non-conventional energy towards sustainability and energy efficiency. 7. Concluding remarks The impinging air jets helps in turbulating the fluid flow with minimal generation of laminar sub layer boundary which otherwise promotes resistance to flow of heat from the heat conveying absorber surface to the working fluid. Marginal increase in the heat transfer has been reported using impinging jets with different geometry and orientations. Also, the friction losses in the solar collector channel air flow get increased but are in controllable limits. The review over such experimental investigations as carried out in the present article has reached the following conclusions:

Based upon the conclusions it is recommended that the performance of solar thermal collector can be increased further using jets of air impinging over the heat transferring absorber surface because of high heat transfer coefficient exhibited compared to that conventional solar thermal collectors. Also, the literature has been found deficient on the thermodynamic analysis of the studies based upon second law of thermodynamics which provides a quality of energy extracted. The thermal, hydraulic and thermohydraulic criteria of performance evaluation thus should be compared simultaneously in order to obtain an energy efficient design of solar thermal systems using MCDM methods. A few of these have been reported in the literature; however a great scope of advancement still exists.

(1) The solar thermal collector performance can be improved using air jets impinging over the heat conveying absorber facade. This is due to the fact that the impingement boundary layer developed in close vicinity of absorber plate are much thinner than developed with conventional parallel fluid flow. However, as the heat transfer augments, the augmentation in frictional losses inside the fluid flow passage is also observed. (2) The variation in the jet diameter reports variation in the Nusselt number, which is found to be highest for jet diameter of 3 mm. The observation has concluded that with further increase in the diameter of the jet, the strength of impingement onto the heat convecting surface gets deteriorated and thus the augmentation in heat transfer coefficient suffers reduction. The 3 mm diameter of the jet is thus an optimum value for maximum heat transfer through impinging jet solar collector passage. (3) The variation in distance between adjoining air jets also presents variation in heat transfer. Where, heat transfer has been observed to be augmenting with increasing jet-to-jet distance, simultaneously the friction factor also increases. Thus, an optimum values of jet-tojet distance both in streamwise and the spanwise direction have to be examined based upon simultaneous consideration of heat transfer as well as friction factor. (4) Heat transfer augmentation with impinging air jets onto the dimpled and/or protruded heat convecting surface has been experimentally studied and reported in the literature. However, the simultaneous observation over the enhancement in frictional losses inside the collector channel have not been reported which is imperative to be examined to determine the overall performance of the impinging jet solar thermal collector. (5) The jets of air impinging over the corrugated (ups and downs) absorber plate have yet not reported in the literature which can marginally prove fruitful for achieving an energy efficient solar thermal collector design. This is due to the fact that the corrugations not only turbulates the fluid inside the passage but also increases the heat transfer surface area and therefore the overall efficiency improvement can be achieved. For this under investigation, the concentration has to be focused on a corrugated design which reports high heat transfer augmentation with minimal augmentation in friction factor. (6) In context to solar thermal collectors, there are two main performance defining criteria which are experimentally determined viz, Nusselt number and friction factor. Both these criteria simultaneously play their role where the first criterion is desired and the second criterion is undesired for effective conversion of one energy

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