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1 Energy ] (]]]]) ]]] ]]] Contents lists available at ScienceDirect Energy journal homeage: Exergetic erformance evaluation and arametric studies of solar air heater M.K. Guta, S.C. Kaushik Centre for Energy Studies, Indian Institute of Technology, Delhi , India article info Article history: Received 28 January 2008 Keywords: Energy and exergy outut Solar air heater Otimum mass flow rate Asect ratio Duct deth abstract The resent study aims to establish the otimal erformance arameters for the maximum exergy delivery during the collection of solar energy in a flat-late solar air heater. The rocedure to determine otimum asect ratio (length to width ratio of the absorber late) and otimum duct deth (the distance between the absorber and the bottom lates) for maximum exergy delivery has been develoed. It is known that heat energy gain and blower work increase monotonically with mass flow rate, while the temerature of air decreases; therefore, it is desirable to incororate the quality of heat energy collected and the blower work. First it is roved analytically that the otimum exergy outut, neglecting blower work, and the corresonding mass flow rate deend on the inlet temerature of air. The energy and exergy outut rates of the solar air heater were evaluated for various values of collector asect ratio (AR) of the collector, mass flow rate er unit area of the collector late (G) and solar air heater duct deth (H). Results have been resented to discuss the effects of G, AR and H on the energy and exergy outut rates of the solar air heater. The energy outut rate increases with G and AR, and decreases with H and the inlet temerature of air. The exergy-based evaluation criterion shows that erformance is not a monotonically increasing function of G and AR, and a decreasing function of H and inlet temerature of air. Based on the exergy outut rate, it is found that there must be an otimum inlet temerature of air and a corresonding otimum G for any value of AR and H. For values of G lesser than otimal corresonding to inlet temerature of air equals to ambient, higher exergy outut rate is achieved for the low value of duct deth and high AR in the range of arameters investigated. If G is high, for an alication requiring less temerature increase, then either low AR or high H would give higher exergy outut rate. & 2008 Elsevier Ltd. All rights reserved. 1. Introduction Solar energy in the form of heat can be collected by using a flat-late collector or a concentrating collector. The flat-late collector is simle in construction, utilizes the beam as well as diffused radiation and does not require tracking. Solar air heater (SAH), because of its simlicity, is chea and is a widely used flatlate collector. The main alications of a solar air heater are sace heating and drying for industrial and agriculture uroses. The energy collection efficiency of solar air heaters has been found to be generally oor because of their inherently low heat-transfer caability between the absorber late and the air flowing in the duct due to unfavorable thermo hysical roerties of air. However, the use of air as a heat-transfer medium instead of water in solar collectors reduces the risks of corrosion, leakage and freezing, and hels to reduce weight and costs of collectors. There are various configuration arameters e.g. number of glass Corresonding author. Tel.: ; fax: addresses: mk_guta70@rediffmail.com (M.K. Guta), kaushik@ces.iitd.ac.in (S.C. Kaushik). cover, emissivity of absorber late, collector length, collector duct deth or distance between absorber and bottom lates in conventional SAH, and the ratio of collector length to collector width i.e. collector asect ratio, etc., affecting the SAH efficiency. The collector asect ratio is the most imortant arameter in the design of any tye of solar air heater. Increasing the collector asect ratio for the same mass flow rate of air er unit surface area of the absorber late increases the air velocity through the duct, which results in more heat transfer to the flowing air as well as ressure dro or required ower consumtion of the um/ blower. The low density and low secific heat of air combined with low heat-transfer coefficient also requires high-volume flow rates that may lead to high friction losses. The design of the flow duct and heat-transfer surfaces of solar air heaters should therefore be executed with the objectives of high heat-transfer rates and low friction losses. Yeh and Lin [1] investigated theoretically as well as exerimentally the effect of collector asect ratio on the energy collection efficiency of flat-late solar air heaters for a constant collector area and different flow rates. They found that energy collection efficiency increases with mass flow rate and collector asect ratio, and theoretical redictions agree reasonably well with the exerimental results. Yeh and Lin /$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi: /j.energy

2 2 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] Nomenclature A c collector area (m 2 ) AR collector asect ratio C secific heat (J/kg K) d e equivalent diameter of duct (m) Ex exergy (W) Ex u exergy outut rate ignoring ressure dro (W) Ex u, exergy outut rate considering ressure dro (W) F 0 collector efficiency factor F r collector heat removal factor f friction factor G mass flow rate er unit collector area (kg/s m 2 ) h enthaly (J/kg), heat-transfer coefficient (W/m 2 K) H solar heater duct deth (m) I radiation intensity (W/m 2 ) IR irreversibility (W) k thermal conductivity (W/m K) L collector dimension, sacing between covers (m) m mass flow rate (kg/s) M number of glass covers Nu Nusselt number ressure (N/m 2 ) Pr Prandtal s number Q heat (W) Re Reynold s number S absorbed flux (W/m 2 ) S g entroy created due to heating of air and ressure dro (W/K) T temerature (K) U heat loss coefficient (W/m 2 K) V velocity (m/s) um work (W) W P Greek symbols a absortivity t Transmissivity b tilt angle of the surface ta transmissivity absortivity roduct d thickness of insulation D ressure dro (N/m 2 ) r density of fluid (kg/m 3 ) m viscosity of fluid (N s/m 2 ) Z efficiency s Stefan s constant e emissivity Subscrits/suerscrits a ambient b back/bottom c collector/late, convection f fluid g glass cover i inner, inlet, insulation l lost, overall loss m mean o outer, outlet/exit late r radiation s side S Sun st stagnation t to T tilted surface u useful w wind N wind 1, 2, 3 length, width, deth of collector [2] investigated the effect of arallel barriers on the energy collection efficiency of flat-late solar air heaters. The barriers divide the air channel into arallel sub-channels or sub-collectors connected in series, and air flows through them in sequentially reversed directions. Thus the effect of increasing the number of arallel barriers is equivalent to increasing the collector asect ratio. Yeh and Lin [3] showed that the energy collection efficiency of a solar air heater can be imroved by oerating several subcollectors with identical asect ratios in series in lace of a single collector with the same total area. They illustrated for two subcollectors that for a constant total collector area, the energy collection efficiency increases and reaches maximum as the two sub-collectors aroach the same area. They also concluded that the imrovement in energy collection efficiency using subcollectors in series increases with increase in insolation and decrease in mass flow rate. The effect of arallel barriers or using the various sub-collectors in series is to increase the velocity of flow as well as heat transfer from absorber surface to flowing air; thus the energy collection efficiency increases. It can be shown that the useful energy gain and ressure dro are strong functions of duct arameters and air flow rate er unit area of late. As enhancement in heat transfer is accomanied by increased ressure dro of flowing air, it is desirable to incororate the ressure dro in analysis. The analytical thermo-hydraulic erformance evaluation of a solar air heater, based on equal uming ower of the collector arrays or sub-collectors arranged in series or arallel mode, has been carried out by Karwa et al. [4]. They varied the duct deth to satisfy the condition of equal uming ower for evaluating the energy efficiency of the series or arallel arrangement of sub-collector modules, and deduced that the configuration with n-sub-collectors in arallel is to be the best for the range of arameters investigated. It is to be noted here that n-sub-collectors in series form the high AR collector. The second law of thermodynamics-based exergy analysis is more suitable to incororate the quality of useful energy outut, and friction losses. The exergy concet based on the second law of thermodynamics rovides an analytic framework for system erformance evaluation. Exergy is the maximum work otential that can be obtained from a form of energy [5,6]. Exergy analysis is a useful method to comlement, not to relace, the energy analysis. Exergy analysis yields useful results because it deals with irreversibility minimization or maximum exergy delivery. Exergy analysis has roven to be a owerful tool in the thermodynamic analysis of energy systems [7,8]. Lior et al. [8] resented the exergy/entroy roduction field equations to analyze the sace- and time-deendent exergy and irreversibility fields in rocesses, and alied these to flow desiccation, combustion of oil drolets, and combustion of ulverized coal. The oularity of the exergy analysis method has grown consequently and is still growing [9 11]. Lior and Zhang [11] attemted to clarify the definitions and use of energy- and exergybased erformance criteria, and of the second law efficiency, to

3 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] 3 advance the international standardization of these imortant concets. In general, more meaningful efficiency is evaluated with exergy analysis rather than energy analysis, since exergy efficiency is always a measure of the aroach to the ideal. Howell and Bannerot [12] analyzed solar collector erformance in terms of otimum outlet temerature, which maximizes the work outut of ideal heat engine cycles utilizing the collector heat outut. This work outut from the useful heat of a solar collector is equal to the exergy outut of the collector for infinite mass flow rate of working fluid, ignoring the ressure dro in the collector. Bejan [13,14] carried out the exergetic analysis without considering frictional ressure dro and using simlified models for a number of simle solar collector systems. For isothermal collectors, he deduced that otimum temerature by neglecting the internal thermal conductance of the collector is the geometric mean of stagnation and ambient temerature; otherwise it is in between the geometric mean of stagnation and ambient temerature, and the stagnation temerature. The stagnation temerature is the maximum temerature attained by the solar collector when there is no flow of working fluid through the solar collector or when useful heat gain is zero. For nonisothermal collectors or ractical collectors, he concluded that the collector fluid must be circulated at a higher rate through collectors with high heat loss or having low stagnation temerature. He also ointed out that irreversibility in the collector varies with mass flow rate and the mass flow rate must be otimum for minimum entroy generation. Manfrida [15] ointed out that to obtain higher exergetic or rational efficiency, the difference between the collector inlet and outlet temeratures should be small for low-erformance collectors and higher for selectivecoated, evacuated or focusing collectors. Kar [16] roved that for maximum exergy outut for the flat-late solar collector for a articular mass flow rate, there is an otimum inlet temerature. Suzuki [17] discussed about the various terms like exergy inflows, exergy leakage and exergy annihilation (destruction) related to the general theory of exergy balance, and alied these to flatlate and evacuated solar collectors. He evaluated the effect of heat caacity on various exergy loss terms and exergy gain by the working fluid. Altfeld et al. [18] discussed the basic concets regarding the exergy analysis of the solar air heater, considering the comression energy needed to overcome ressure dro. They evaluated the various losses during the collection of solar energy and reresented in the form of energy and exergy flow diagrams. They considered the net exergy flow as a suitable quantity for balancing the useful energy and friction losses, and for the otimum design of absorber and flow ducts. They also determined an otimum flow velocity for maximizing the net exergy gain. The second law otimization of different absorber models for constant ambient temerature and global radiation, and for fixed high mass flow rates were carried out by Altfeld et al. [19]. However, the analysis given therein is imlicit and not easy to follow, and could not be further used for other systems. The geometry of rib roughness considered by them is not suitable for frictional ower consideration as it is unnecessary to use ribs on the bottom late for a solar air heater. Torres-Reyes et al. [20] followed the nonisothermal model given by Bejan [14] and resented the rocedure to establish the otimal erformance arameters for minimum entroy generation during the collection of solar energy. They evaluated stagnation temerature, mass flow number, minimum entroy generation number and the otimal mass flow rate of the working fluid and alied the develoed rocedure to a tyical solar drier. Luminosu and Fara [21] carried out the exergy analysis-based numerical simulation by exressing the exergy efficiency as a function of mass flow rate and collector area; they obtained the otimum area by taking the inlet temerature equal to ambient temerature and assuming a constant value of the overall loss coefficient. They determined the local otimum mass flow rate for each area of the collector from a range of considered flow rates; and for the area ranging from 0 to 10 m 2 and for a mass flow rate from 0 to kg/s, they evaluated the global otimum mass flow rate and area. It may be noted here that the exression for heat gain or exergy outut of the collector is a function of mass flow rate er unit area. They also analyzed the influence of the heat loss coefficient, glass quality, solar flux density and secific heat of fluid on the flat solar collector exergy, heat gain, exergy efficiency and temerature rise of the fluid through the collector. The analyzed relevant literatures contain studies on the deendences of the exergy outut on fluid mass flow rate and temerature of fluid at inlet to the collector. It has been recommended [1 3] to use high AR and mass flow rate on the basis of energy analysis; thus the aim of the resent investigation is, to determine the effect of G, AR, and H on energy as well as on exergy outut rate. 2. Theoretical analysis 2.1. Analysis of solar air heater The collector under consideration consists of a flat glass cover and a flat absorber late with a well insulated arallel bottom late, forming a assage of high duct asect ratio (the ratio of collector width to collector duct deth) through which the air to be heated flows as shown in Fig. 1. The heat gain by air may be calculated by the following equations: Q u ¼ A c ½S U l ðt m T a ÞŠ ¼ A c ½t g a I T U l ðt m T a ÞŠ (1) Q u ¼ mc ðt o T i Þ (2) Q u ¼ A c F r ½S U l ðt i T a ÞŠ (3) where F r is collector heat removal factor and is given by F r ¼ mc ½1 e ðu lacf 0 Þ=mc Š (4) U l A c x dx Ex c,s Control-volume U t Glass-cover T i Bottom-late T f T f + dt f To H Absorber late L 3 P Ex W L 1 Ex o L 2 Insulation Ex i Fig. 1. Flat-late solar air heater.

4 4 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] The collector efficiency factor F 0 is F 0 ¼ 1 þ U 1 l (5) h e and the equivalent heat-transfer coefficient h e is h r; bh c;f b h e ¼ h c;f þ (6) ðh r; b þ h c;f b Þ The mean absorber late temerature from Eqs. (1) and (3) is given by Q u T m ¼ T a þ Q l ¼ T U l A i þ ð1 F r Þ where c A c F r U l Q l ¼ SA c Q u (7) The mean fluid temerature (T m ), is given by T m ¼ 1 Z L1 T L f dx ¼ T i þ Q u 1 F r 1 0 A c F r U l F 0 (8) 2.2. Heat transfer and ressure dro The overall heat loss coefficient U l is the sum of U b, U s and U t,of which U b and U s for a articular collector can be regarded as constant while U t varies with temerature of the absorber late, number of glass covers and other arameters. The to heat loss coefficient U t is evaluated emirically [22] by " # M U t ¼ ðc=t m Þ½ðT m T a Þ=ðM þ f 0 ÞŠ þ 1 1 0:252 h w " sðt 2 m þ þ T2 a ÞðT # m þ T a Þ ½1=ð þ 0:0425Mð1 ÞÞŠ þ ½ð2M þ f 0 (9) 1Þ= c Š M in which f 0 ¼½ð9=h w Þ ð9=h 2 w ÞŠðT a=316:9þð1 þ :091MÞ, C ¼ 204:429ðcos bþ 0:252 =L 0:24 and the heat-transfer coefficient at the to of the cover due to wind is h c;c a ¼ h w ¼ 5:7 þ 3:8V 1 (10) The overall heat loss coefficient is given by U l ¼ U b þ U s þ U t in which U b ¼ k i and U s ¼ ðl 1 þ L 2 ÞL 3 k i (11) d b L 1 L 2 d s The radiation heat-transfer coefficient h r; b between the absorber late and the bottom late is given by sðt 4 m h r; b ðt m T bm Þ¼ T4 bm Þ (12) ½ð1= Þþð1= b Þ 1Š For small temerature difference between T m and T bm on the absolute scale, the above equation can be written as 4sT 3 av h r; b ffi ½ð1= Þþð1= b Þ 1Š where T av ¼ðT m þ T bm Þ=2 and T av is taken equal to T m in iterative calculation using the same logic. For smooth duct the convection heat-transfer coefficients between, flowing air and absorber late h c;f, and flowing air and bottom late h c;f b are assumed equal. The following correlation for air, for fully develoed turbulent flow (if the length to equivalent diameter ratio exceeds 30) with one side heated and the other side insulated [23], is aroriate: Nu ¼ h c;f d e k a ¼ 0:0158ðReÞ 0:8 (13a) If the flow is laminar, then following correlation by Mercer [24] for the case of arallel smooth lates with constant temerature on one late and the other late insulated is aroriate: Nu ¼ h c;f d e 0:0606½Re Pr ðd e =L 1 Þ 0:5 Š ¼ 4:9 þ (13b) k a 1 þ 0:0909½Re Pr ðd e =L 1 Þ 0:7 ŠðPrÞ 0:17 The characteristic dimension or equivalent diameter of duct is given by d e ¼ 2L 2H (14) ðl 2 þ HÞ The Reynolds number Re is calculated by Re ¼ rvd e m ¼ r m 2L 2 H m L 2 Hr ðl 2 þ HÞ ¼ 2m (15) mðl 2 þ HÞ The ressure loss D through the air heater duct, is D ¼ 4fL 1V 2 r (16) 2d e If Re ¼ðrVd e =mþ2300, i.e. laminar flow, then the coefficient of friction is calculated by f ¼ 16 (17a) Re otherwise the coefficient of friction f for the turbulent flow in a smooth air duct is calculated from the Blasius equation, which is f ¼ 0:0791ðReÞ 0: Energy and exergy outut rate (17b) The useful energy or heat gain by air is given by Q u ¼ A c F r ½S U l ðt i T a ÞŠ ¼ mc ðt o T i Þ¼A c ½t g a I T U l ðt m T a ÞŠ The law of exergy balance [5,6], considering SAH (Fig. 1) as a control volume (CV), can be written as Ex i þ Ex c;s þ Ex W ¼ Ex o þ IR (18) where Ex i and Ex o are the exergy associated with the mass flow of air entering and leaving the CV; Ex c,s is the exergy of solar radiation falling on glass cover; Ex W is the exergy of work inut required to um the air through SAH, and IR is irreversibility or exergy loss of the air heating rocess. The heat flux is received from the sun and collected by air flowing through the solar air heater. The irreversibility occurs at various stages like: flux falling on the transarent cover, absortion by the absorber surface and heat loss to ambient. The useful exergy gain Ex u,, considering ressure dro or blower work, by air is calculated by Ex u; ¼ Ex o Ex i Ex W ¼ mc ðt o T i Þ T a ln T o T a W (19) T i T i The ½mc lnðt o =T i ÞþðW =T i ÞŠ ¼ S g is the sum of entroy created due to the heating of air and ressure dro or um/blower work. The um (blower) work W is calculated by W ¼ md (20) ðz m rþ The um-motor efficiency Z m is considered equal to 0.85.

5 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] 5 Table 1 Proerties of air T (1C) r (kg/m 3 ) C (KJ/kg K) m 10 6 (N s/m 2 ) k (W/m K) (Pr) Otimum mass flow rate for maximum exergy outut rate ignoring um work The exergy outut rate (Eq. (19)) besides um work also deends on the useful heat gain, inlet temerature of air and temerature increase of air. Thus there should be an otimum flow rate for a given inlet temerature of air and ambient condition. At no-flow condition the quantity and quality of heat energy collected are zero, while at infinite flow rate couled with near-ambient inlet temerature of air, the quality (exergy) of heat energy collected reduces. If the Bliss equation is used for the collector then Q u ¼ A c F 0 ðt S U i þ T o Þ l T a ¼ mc ðt o T 2 i Þ (21) Fig. 2. Variation of useful heat gain and T a S g for a fixed value of solar radiation intensity for (a) low and (b) high inlet temerature of air.

6 6 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] Writing, logðt o =T i Þffið2ðT o T i ÞÞ=ðT o þ T i Þ, as T o =T i 2 (for SAH), in the exergy outut equation (19) by ignoring ressure dro, then the Ex u, exergy outut, ignoring ressure dro is 2ðT o T Ex u ¼ Q u mc T i Þ a ðt o þ T i Þ ¼ Q u 1 2T a ðt o þ T i Þ Ex u ¼ A c F 0 ðt S U i þ T o Þ l T a 2 1 2T a ðt o þ T i Þ (22) For maximum exergy outut differentiating Ex u w.r.t ðt o þ T i Þ=2 and substituting equal to zero we get T o þ T 2 i ¼ T a T a þ S )ðt o þ T 2 U i Þ ot ¼ 2 ffiffiffiffiffiffiffiffiffiffiffi T a T st, l where ½T a þðs=u l ÞŠ ¼ T st is the stagnation temerature. Substituting ðt o þ T i Þ ot in Eq. (21) and solving for m we get ffiffiffiffiffiffiffiffiffiffiffi. ffiffiffiffiffiffiffiffiffiffiffi m ot ¼ A c F 0 fs U l ½ T a T st T a Šg 2c ð T a T st T i Þ Putting S ¼ U l ðt st T a Þ we get m ot ¼ A c F 0 U l ðt st ffiffiffiffiffiffiffiffiffiffiffi. ffiffiffiffiffiffiffiffiffiffiffi T a T st Þ 2c ð T a T st T i Þ Case I: ift i ¼ T a then m ot ¼ A c F 0 U l T st ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffi ffiffiffiffiffi T a T st.2c T a T st T a ¼ A c F 0 U l T st.2c T a From the above relation we can say that m must be finite. Fig. 3. Variation of exergy outut rate and heat gain rate with mass flow rate, for solar radiation intensity 950 W/m 2, for (a) low and (b) high inlet temerature of air.

7 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] 7 Case-II: ift i ¼ðT a þ ffiffiffiffiffiffiffiffiffiffiffi T a T st Þ=2 then m ot ¼ A c F 0 U l ðt st ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi T a T st Þ.2c T a T st T a þ ffiffiffiffiffiffiffiffiffiffiffi T a T st 2 ffiffiffiffiffiffi ffiffiffiffiffi ¼ A c F 0 U l T st.c T a From the above relation we can say that m must be finite and is about twice that of the revious case. Case III: ift i! ffiffiffiffiffiffiffiffiffiffiffi T a T st then the m ot tends to infinity Case IV: ift i! T st then the m ot tends to zero. As for this case m ot ¼ A c F 0 U l ðt st ffiffiffiffiffiffiffiffiffiffiffi. ffiffiffiffiffiffiffiffiffiffiffi T a T st Þ 2c ð T a T st T st Þ¼ A c F 0 U l =2c Thus m ot becomes negative or at such high inlet temerature there is no more ositive exergy gain with flow, i.e. the flow rate should be zero. It is evident that m ot first increases with inlet temerature and then decreases. It can also be roved that the maximum exergy outut for a solar intensity is achieved for an inlet temerature higher than ambient temerature. By substituting the ðt o þ T i Þ ot ¼ 2 ffiffiffiffiffiffiffiffiffiffiffi T a T st in Eq. (22) and solving, the otimum exergy outut obtained is ðex u Þ ot ¼ Q u ½1 ð1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðt a =T st ÞÞŠ and from this relation it can be concluded that for otimum exergy outut (Ex u ) ot the heat energy gain or mass flow rate must be very high and thus the inlet temerature must be the geometric mean of ambient and stagnation temerature. The (Ex u, ) ot will be at inlet temerature lower than ffiffiffiffiffiffiffiffiffiffiffi T a T st as the um work (Eqs. (16), (20)) Fig. 4. Variation of (a) exergy outut rate and (b) heat gain rate, with mass flow rate and inlet temerature of air, for a solar radiation intensity of 600 W/m 2.

8 8 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] becomes significant at a higher mass flow rate. As for a solar air heater, the inlet temerature is generally equal to ambient temerature; thus for maximum exergy outut, the mass flow rate must be low, but if the inlet temerature is high (may be for collectors in series) then the mass flow rate may be ket high. The solar absorbed flux or T st varies throughout the day, thus for otimum exergy outut the mass flow rate should be controlled accordingly, as it is unractical to control the inlet temerature. 3. Numerical calculations For a collector configuration, system roerties and oerating conditions numerical calculations have been carried out to evaluate the energy/exergy outut rate of a solar air heater, for various values of collector asect ratio (AR) of the collector, mass flow rate er unit area of the collector late (G) and solar air heater duct deth (H). The air heater length and width are calculated by L 1 ¼ðA c ARÞ 0:5 and L 2 ¼ A c =L 1, resectively, where AR is the asect ratio of the collector. In order to obtain the results numerically, codes have been develoed in Matlab-7 using the following fixed arameters, unless otherwise mentioned: A c ¼ 2m 2, K i ¼ 0.05 W/m K, L ¼ 4 cm, d b ¼ 6 cm, d s ¼ 4 cm, e ¼ 0.95, e c ¼ 0.88, e b ¼ 0.95, a ¼ 0.95, t g ¼ 0.88, b ¼ 30 o, T i ¼ 30 1C, T a ¼ 30 1C, V N ¼ 2.5 m/s, I T ¼ 600 and 950 W/m 2, H ¼ 1 8 cm, AR ¼ and G ¼ kg/h-m 2. In order to evaluate the energy/exergy outut rate of the collector, first initial values of T m and T m are assumed according to the inlet temerature of air and various heat-transfer coefficients are calculated using Eqs. (9) (15), and at temorary value of useful heat gain is estimated from Eqs. (3) (6). The new values of T m and T m are calculated using Eqs. (7) and (8). If the calculated new values of T m and T m are different from the reviously assumed value, then the iteration is continued with the new values till the absolute differences of the new value and the revious value of mean late temerature as well as mean fluid temerature are less than or equal to Air roerties are determined at T m by interolation from air roerties [25] given in Table 1. Finally calculated values of T m and T m are used to evaluate the energy/exergy outut rate using Eqs. (16), (17), (19) Fig. 5. Variation of heat energy outut rate with mass flow rate, for various values of AR, for (a) solar radiation intensity 950 W/m 2 and 1.5 cm duct deth, and (b) solar radiation intensity 600 W/m 2 and 2.5 cm duct deth. Fig. 6. Variation of exergy outut rate with mass flow rate, for various values of AR, for (a) solar radiation intensity 950 W/m 2 and 1.5 cm duct deth, and (b) solar radiation intensity 600 W/m 2 and 2.5 cm duct deth.

9 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] 9 and (20). It has been reorted [1] that theoretical redictions for energy outut rate/thermal efficiency agree reasonably well with the exerimental results. By sensitivity analysis it has been found that differences from the values of to heat loss coefficient, heat-transfer coefficient due to convection and coefficient of friction in the order of 75% have only small effects on the trend of variation of energy as well as exergy outut rate. Sensitivity analysis shows that maximum 5% uncertainty in to heat loss coefficient changes the energy outut rate in the range of % and exergy outut rate by 2.5 6%; the larger variations are with very small flow rates. The energy outut rate and exergy outut rate change u to 1.7% and 3%, resectively, with 5% change in the value of heat-transfer coefficient due to convection, given by the used correlations. The uncertainty in the determination of coefficient of friction has no effect on the energy outut rate, while the exergy outut changes u to 1.5% and 4.75%, for 5% and 15% change in the value of coefficient of friction; the higher variations occur at large mass flow rates. 4. Results and discussion rates of increase of both terms are almost same but the magnitude of heat gain is more than the entroy created term (T a S g )uto very high mass flow rates; thus the exergy outut increases with mass flow rate u to very high values of mass flow rate. The variations of exergy outut rate and heat gain rate with mass flow rate are shown in Fig. 3(a) and (b), for the inlet temeratures equal to 303 and 340 K, resectively, for the same values of solar intensity, collector asect ratio and duct deth. For low inlet temerature the exergy outut rate first increases, attains its maximum value and after that it decreases with mass flow rate in the laminar flow regime; the exergy outut rate also decreases in the turbulent flow regime but at flow transition there is an increase in the exergy outut rate due to the different correlations of heat-transfer coefficient and friction factor for laminar and turbulent flow. For high inlet temerature, the exergy outut rate increases continuously u to some mass flow rate in turbulent flow, though the rate of change of exergy outut rate decreases with the value of mass flow rate; and at very high flow rate, the exergy outut will become zero due to increased ressure dro. Fig. 3 and mathematical relations 2, 3 and 19 indicate that there should be a global otimum inlet temerature for a articular 4.1. Variations of useful heat energy gain, roduct of ambient temerature and sum of entroy created due to heating of air and ressure dro (T a S g ); energy and exergy outut rate with mass flow rate and inlet temerature of air The variations of heat energy gain and T a S g with mass flow rate are lotted in Fig. 2(a) and (b), for low and high inlet temerature of air, resectively, for a fixed values of solar radiation intensity, collector asect ratio and duct deth. The numerical values of both terms are high for low inlet temerature and low for high inlet temerature of air. It is also clear from Fig. 2 that the heat gain increases with mass flow rate and decreases with the inlet temerature of fluid; but the difference of heat energy gain and T a S g, which is exergy outut, does not follow this trend. For low inlet temerature the rate of increase of entroy created term (T a S g ) is more than the rate of increase in heat gain rate after a certain mass flow rate, and thus there is an otimum mass flow rate at low value, as roved theoretically earlier by ignoring um work. If the temerature is high then the Table 2 Otimum G, corresonding energy outut, exergy outut and flow Reynolds number with AR for H ¼ 1.5 cm, I T ¼ 950 W/m 2 and T i ¼ 303 K AR Otimum G Q Ex Re Fig. 7. Variation of exergy outut rate with mass flow rate, for various values of H, for (a) solar radiation intensity 950 W/m 2 and AR ¼ 3, and (b) solar radiation intensity 600 W/m 2 and AR ¼ 4.

10 10 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] solar intensity. It can be observed from Fig. 3 that the maximum exergy outut for low inlet temerature is less than 40 W while for high it is more than 80 W, and for very high value of inlet temerature the heat gain and thus exergy outut may become negative. Using Eqs. (2) and (3) the T o from Eq. (19) can be eliminated. The resulting equation for exergy outut is a function of inlet temerature and other arameters. If other arameters (F r, U l ) are treated constant then there should be an otimum T i for a articular m and I. The variations of energy outut or heat gain rate, and exergy outut rate, with mass flow rate and inlet temerature, are shown in Fig. 4(a) and (b), resectively. The values of collector asect ratio and duct deth are taken to be the same while the solar radiation intensity is different. It is evident from Fig. 4(a) that heat gain rate increases with mass flow rate, and decreases with inlet temerature. It is clear from Fig. 4(b) that there is a global otimum inlet temerature that maximizes the exergy outut for a given value of solar radiation intensity. The increase in exergy outut (Fig. 4) with mass flow rate for any T i is not significant after a certain value of mass flow rate in the low range. It can be concluded from Figs. 3 and 4 that both energy as well as exergy outut rate decrease as the solar intensity reduces Variations of useful heat energy and exergy outut rates for various asect ratios of the solar collector with mass flow rate The energy and exergy outut rates were evaluated for various values of collector asect ratio (AR) and mass flow rate er unit area of the collector late (G). The inlet temerature of air is taken equal to ambient temerature. Fig. 5(a) and (b) shows the imrovement in energy outut rate with AR and G as ointed by other investigators. The increase in energy outut rate with G is more for a higher value of AR. It is evident from Fig. 5 that the energy outut rate increases as AR increases. The enhancement in the energy outut rate is due to the fact that increase in AR or G results in increased velocity of flow due to the reduction of crosssectional area of the collector duct or increase in mass flow rate, accomanied with enhanced convective heat-transfer coefficient Fig. 8. Variation of exergy outut rate with mass flow rate, for various values of H, for (a) solar radiation intensity 950 W/m 2 and AR ¼ 3, and (b) solar radiation intensity 600 W/m 2 and AR ¼ 4. Fig. 9. Variation of temerature increase of air with mass flow rate (a) for various values of AR and (b) for various values of H.

11 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] 11 through the duct. It can be concluded that for better energetic erformance the G and AR must be high. However, the energetic analysis view oint comletely ignores the um/blower work requirement and quality of heat energy collected. Fig. 6(a) and (b) shows the variation of exergy outut rate with AR and G, and it is evident from this figure that the exergy outut rate does not increase monotonically with G (as roved earlier for a low inlet temerature of air), and AR. For low mass flow rate, the exergy outut rate increases with AR u to larger values of AR. Thus higher AR may be used to gain otimum exergy outut for a low inlet temerature of air. It is clear from Fig. 6 that for higher values of G, the exergy outut rate decreases with G and AR. This rate of decrease of exergy outut with higher G increases with AR. Thus, for maximum exergy outut, the AR should not be more if G is high. It can be understood from Fig. 6 that the otimum G deends on AR; thus the variations of otimum G and corresonding energy outut, exergy outut and flow Reynolds number with AR are given in Table 2. It can be seen from Table 2 that as AR increases, the otimum G first increases due to transition or turbulent flow and then decreases; for higher AR the otimum exergy outut also decreases Variations of useful heat energy and exergy outut rate for various duct deths of the solar collector with mass flow rate Figs. 7(a) and (b), and 8(a) and (b) show the variation of energy and exergy outut rates, resectively, with mass flow rate er unit area of the collector late (G) for various values of duct deth (H). The inlet temerature of air is taken equal to ambient Fig. 10. Variation of um work with mass flow rate of air (a) for various values of AR and (b) for various values of H.

12 12 M.K. Guta, S.C. Kaushik / Energy ] (]]]]) ]]] ]]] temerature. It is evident from Fig. 7 that the energy outut rate is high at lower values of duct deth, regardless of the other arameters, and for higher energetic erformance the duct deth should be low. The exergy outut rate does not show monotonous trend (Fig. 8) with decrease in duct deth; it deends on AR and G. AtlowG the exergy outut rate is also high for lesser duct deth, but it decreases at a faster rate with G for low duct deth. Thus, for the maximum exergy outut the H should be low only if G is low Variations of temerature rise of air and um work with G, AR and H: imortance of exergy Fig. 9(a) shows the variation of temerature increase of air with G and AR, while Fig. 9(b) shows the variation of temerature increase of air with G and H. As high temerature increase is more useful as er utility view oint, it can be said that G must be very low. But at very low value of G the useful heat gain will also be very small. The temerature rise for a given flow rate changes more with H in comarison to AR; it may be said that AR must be very high and H must be low. The variation of required um work with G and AR is shown in Fig. 10(a), while Fig. 10(b) shows the variation with G and H. It is evident that the required um work increases with increase in G and AR, and decrease in H as er the ower law. It is also clear from Fig. 10 that for extreme values of G, AR and H, the required um work becomes quite high. It even exceeds the maximum exergy outut, ignoring the ressure dro that can be obtained for the given solar radiation intensity. The temerature rise criterion alone recommends the use of very low H and G; but in order to get significant energy outut the G must be finite. The energy outut criterion recommends using high AR and G, and low H. For higher values of G, not only the temerature rise of air or usefulness reduces, but the um work may also become significant. Thus to incororate the quality of heat energy collected and required um work, the second law-based exergy is a suitable quantity. The energy-based criteria do not give the otimum values of G, AR and H; hence otimal erformance arameters, for articular alication of SAH, should be decided using the exergy outut. 5. Conclusion It can be said that as er the energy outut rate evaluation criterion the solar air heater should have high AR and G, and low duct deth and low inlet temerature of air. The exergy outut deends on heat gain and entroy created term; thus it incororates the temerature rise of air and um work. It has been roved and observed that if the inlet temerature of air is low than maximum exergy outut is achieved at low value of mass flow rate but if inlet temerature of fluid is high then exergy outut increases with mass flow rate though gain at very high mass flow rate is not significant. It has also been deduced that for otimum exergy outut ignoring the ressure dro the otimum inlet temerature is geometric mean of ambient and stagnation temerature, while for otimum exergy outut considering the ressure dro, the otimum inlet temerature is lesser than this geometric mean and more than ambient. For air heater alications, the inlet temerature is generally ambient and may be more for collectors in series; a slight high flow rate may be ket for the latter case. The exergy outut rate evaluation criterion shows that there will be otimum values of AR and H; and otimum deends on G to suit a articular alication. As air heater alications are governed by temerature rise required or mass flow rate, the decision should be made by requirement of alication. In the case of air heater, the required um work increases raidly with G; thus if G is low then high AR and low H will give higher exergy outut, while for higher G the reverse is true. References [1] Yeh HM, Lin TT. The effect of collector asect ratio on the energy collection efficiency of flat-late solar air heaters. Energy 1995;20: [2] Yeh HM, Lin TT. Efficiency imrovement of flat-late solar air heaters. Energy 1996;21: [3] Yeh HM, Lin TT. Solar air heaters with two collectors in series. Energy 1997;22: [4] Karwa R, Garg SN, Arya AK. Thermo-hydraulic erformance of a solar air heater with n-sub-collectors in series and arallel configuration. Energy 2002;27: [5] Kotas TJ. The exergy method of thermal lant analysis. Butterworths; [6] Bejan A. Advanced engineering thermodynamics. Wiley Interscience Pub; [7] Kaushik SC, Mishra RD, Singh N. Second law analysis of a solar thermal ower system. Int J Sol Energy 2000;20: [8] Lior N, Sarmiento-Darkin W, Al-Sharqawi Hassan S. The exergy fields in transort rocesses: their calculation and use. Energy 2006;31: [9] Rosen MA, Dincer I. A study of industrial steam rocess heating through exergy analysis. Int J Energy Res 2004;28: [10] Kanoglu M, Dincer I, Rosen MA. Understanding energy and exergy efficiencies for imroved energy management in ower lants. Energy Policy 2007;35: [11] Lior N, Zhang N. Energy, exergy, and Second Law erformance criteria. Energy 2007;32: [12] Howell JR, Bannerot RB. Otimum solar collector oeration for maximizing cycle work outut. Sol Energy 1977;19: [13] Bejan A. Extraction of exergy from solar collectors under time-varying conditions. Int J Heat Fluid Flow 1982;3: [14] Bejan A. Entroy generation through heat and fluid flow. New York: Wiley- Interscience; [15] Manfrida G. The choice of an otimal working oint for solar collectors. Sol Energy 1985;34: [16] Kar AK. Exergy efficiency and otimum oeration of solar collectors. Al Energy 1985;21: [17] Suzuki A. General theory of exergy-balance analysis and alication to solar collectors. Energy 1988;13: [18] Altfeld K, Leiner W, Fiebig M. Second law otimization of flat-late solar air heaters art l: the concet of net exergy flow and the modeling of solar air heaters. Sol Energy 1988;41: [19] Altfeld K, Leiner W, Fiebig M. Second law otimization of flat-late solar air heaters. Part 2: Results of otimization and analysis of sensibility to variations of oerating conditions. Sol Energy 1988;41: [20] Torres-Reyes E, Cervantes-de Gortari JG, Ibarra-Salazar BA, Picon-Nunez M. A design method of flat-late solar collectors based on minimum entroy generation. Exergy Int J 2001;1: [21] Luminosu I, Fara L. Determination of the otimal oeration mode of a flat solar collector by exergetic analysis and numerical simulation. Energy 2005;30: [22] Malhotra A, Garg HP, Palit A. Heat loss calculation of flat lat solar collectors. J Therm Energy 1981;2:2. [23] Kays WM. Convective heat and mass transfer. New York: McGraw-Hill; [24] Duffie JA, Beckman WA. Solar engineering of thermal rocesses. New York: Wiley; [25] Sukhatme SP. Solar energy: rinciles of thermal collection and storage. New Delhi: Tata McGraw-Hill; 1987.