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1 This article was downloaded by:[james Cook University] On: 14 November 2007 Access Details: [subscription number ] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Journal of Green Energy Publication details, including instructions for authors and subscription information: A Parametric Study on the Thermal Performance of a Solar Air Collector with a V-Groove Absorber Tao Liu a ; Wenxian Lin ab ; Wenfeng Gao a ; Chuanxu Luo a ; Ming Li a ; Qinhong Zheng a ; Chaofeng Xia a a Solar Energy Research Institute, Yunnan Normal University, Kunming, P. R. China b School of Engineering, James Cook University, Townsville, Australia Online Publication Date: 01 November 2007 To cite this Article: Liu, Tao, Lin, Wenxian, Gao, Wenfeng, Luo, Chuanxu, Li, Ming, Zheng, Qinhong and Xia, Chaofeng (2007) 'A Parametric Study on the Thermal Performance of a Solar Air Collector with a V-Groove Absorber', International Journal of Green Energy, 4:6, To link to this article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 International Journal of Green Energy, 4: , 2007 Copyright Taylor & Francis Group, LLC ISSN: print / online DOI: / A PARAMETRIC STUDY ON THE THERMAL PERFORMANCE OF A SOLAR AIR COLLECTOR WITH A V-GROOVE ABSORBER Tao Liu Solar Energy Research Institute, Yunnan Normal University, Kunming, P. R. China Wenxian Lin Solar Energy Research Institute, Yunnan Normal University, Kunming, P. R. China and School of Engineering, James Cook University, Townsville, Australia Wenfeng Gao, Chuanxu Luo, Ming Li, Qinhong Zheng, and Chaofeng Xia Solar Energy Research Institute, Yunnan Normal University, Kunming, P. R. China In this paper, a parametric study on the thermal performance of a solar air collector with a v-groove absorber has been investigated. In this single-cover collector, the air flowing in the channel formed by the v-groove absorber and the bottom plate which is flat and insulated is along the groove, aiming at enhanced heat transfer rate between the air and the absorber by increasing the heat transfer surface area, which is crucial to the improvement of thermal performance of a solar air collector. To quantify the achievable improvements with the v-groove absorber, a flat-plate solar air collector where both the absorbing plate and the bottom plate are flat, is also considered. The thermal performance of these two types of solar air collectors is analyzed and compared under various configurations and operating conditions. The results show that the v-groove collector has considerably superior thermal performance to the flat-plate collector. It is also found that to achieve better thermal performance, it is essential to; use a small size of the v-groove absorber for the v-groove absorber collector and to maintain a small gap between the absorber and the bottom plate for the flat-plate collector; to use selected coatings that have a very high absorptivity of solar radiation but a very small emissivity of thermal radiation on the absorber and glass cover; to maintain an air mass flow rate above 0.1kg/m 2 s; and to operate the collectors with the inlet fluid temperature close to that of the ambient fluid. Keywords: Solar air collector; Thermal performance; V-groove absorber; Flat-plate absorber; Analytical solution INTRODUCTION Solar air collectors are key components in many engineering applications (Duffie and Beckman, 1991), such as in building heating systems, in solar drying devices, etc. Due to the poor thermal conductivity and small heat capacity of air, the convective heat transfer Address correspondence to Wenxian Lin, School of Engineering, James Cook University, Townsville, QLD 4811, Australia. wenxian.lin@jcu.edu.au. 601

3 602 LIU ET AL. rate inside the air flow channel formed by the absorbing plate and the bottom plate, where the air is heated, is low, and a great deal of effort has been made to increase this rate (Williams, 1983). Among the many effective ways to augment the convective heat transfer rate in channel flows, those that increase the heat transfer surface area and those that increase turbulence inside the channel with fins or corrugated surfaces have been the most popular (Goldstein and Sparrow, 1976, 1977) and many studies have been carried out on them. For example, the convective heat transfer in a v-groove linear solar collector by was studied by Meyer et al. (1982) while the natural convection in a channel formed by a v-groove surface and a flat plate was studied numerically and experimentally by Zhao and Li (1991). Stasiek (1998) carried out experimental studies on the heat transfer and fluid flow across corrugated-undulated heat exchanger surfaces. Piao (1992) and Piao et al. (1994) investigated experimentally the natural, forced and mixed convective heat transfer in a cross-corrugated channel solar air collector. Noorshahi et al. (1996) conducted a numerical study on the natural convection in a corrugated enclosure with mixed boundary conditions. Gao (1996) and Gao et al. (2000) numerically simulated the natural convection inside the channel formed by a flat cover and a wave-like absorbing plate. Karim and Hawlader (2006) evaluated, both analytically and experimentally, the thermal performance of a v-groove solar air collector under the meteorological conditions of Singapore. In this paper, a comprehensive parametric study has been carried out to investigate the thermal performance of a solar air collector with a v-groove absorber under a wide range of configurations and operating conditions, aiming at providing important and useful information for the optimal design of such air collectors in engineering applications. Comparisons have also been made to that of a flat-plate solar air collector with a flat absorber to show the efficiency improvement achievable with the use of the v-groove absorber. THEORETICAL ANALYSIS The solar air collector under consideration consists of a single flat glass cover, a v-groove absorber and a flat bottom plate that is attached by a back insulation underneath. The channel formed by the absorber and the bottom plate is the air flow channel where the air is heated by the absorbed solar radiation on the absorber. As sketched in Figure 1, the Figure 1 Schematic description of the v-groove absorber solar air collector (a), which has a v-groove absorber and a flat bottom plate and the flat-plate solar air collector (b), which has both a flat absorber and a flat bottom plate.

4 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 603 air flows along the groove. The aim of the use of the v-groove absorber, as mentioned above, is to enhance the heat transfer rate inside the air flow channel by increasing the heat transfer surface area, which is crucial to the improvement of efficiencies of solar air collectors. To quantify the achievable improvements with the v-groove absorber, a flat-plate solar air collector, where both the absorber and the bottom plate are flat, is also analyzed. To model the collectors considered, a number of simplifying assumptions can be made to lay the foundations without obscuring the basic physical situation. These assumptions are as follows: Thermal performance of collectors is steady state. There is a negligible temperature drop through the glass cover, the absorbing plate, and the bottom plate. There is one-dimensional heat flow through the back insulation, which is in the direction perpendicular to the air flow. The sky can be considered as a blackbody for long-wavelength radiation at an equivalent sky temperature. Loss through the front and back surfaces are to the same ambient temperature. Dust and dirt on the collectors and the shading of the collector absorbing plates are negligible. Thermal inertia of collector components is negligible. Operating temperatures of collector components and mean air temperatures in air channels are all assumed to be uniform. Temperature of the air varies only in the flow direction. All air channels are assumed to be free of leakage. Thermal losses through the collector backs are mainly due to the conduction across the insulation and those caused by the wind and the thermal radiation of the insulation are assumed to be negligible. Energy Balance Equations The thermal network for both the v-groove collector and the flat-plate collector considered in this paper is illustrated in Figure 2. If the solar insolation rate incident on the glass cover is I (W/m 2 ), the transmissivity of solar radiation of the glass cover is τ c, and the absorptivity of solar radiation of the absorbing plate is α ap, the solar radiation absorbed by the absorbing plate per unit area, S (W/m 2 ), which is equal to the difference between the incident solar radiation and the optical loss, is calculated by (Duffie and Beckman, 1991): S@ 097. t α I, (1) c ap where the factor 0.97 represents the averaged transmittance-absorptance product. This absorbed energy S is distrubuted to thermal losses through the glass cover and the bottom plate and to useful energy gain q u (W/m 2 ), which heats the air in the channel from the inlet temperature T fo (K) to the outlet temperature T fo (K), resulting in a mean air temperature T f = (T fi + T fo )/2. On the glass cover, the energy gains are α c I, where α c is the absorptivity of solar radiation of the glass cover, the heat transferred by natural convection from the absorbing plate to the glass cover is represented by h c,ap-c (W/m 2 K), which is the convection heat

5 604 LIU ET AL. Figure 2 Thermal network for the single cover solar air collector. transfer coefficient between the glass cover and the absorbing plate, and the heat transferred by thermal radiation from the absorbing plate is represented by h r,ap-c (W/m 2 K), which is the radiation heat transfer coefficient between the cover and the absorbing plate. The energy losses through the glass cover are the heat transferred by the convection due to wind represented by h w (W/m 2 K), which is the wind convection heat transfer coefficient, and the heat transferred by the thermal radiation from the cover to the sky at T s (K) represented by h r,c-s (W/m 2 K), which is the radiation heat transfer coefficient between the cover and the sky. Hence, the energy balance in the glass cover requires, a c I + h c,ap-c + h r,ap-c T ap T c = h w + h r,c-s T c T a ( )( ) ( )( ), (2) where T ap (K) and T c (K) are the mean temperature on the absorbing plate and on the glass cover, and T a (K) is the ambient temperature. On the absorbing plate, the absorbed solar radiation S is distributed to thermal losses to the glass cover by natural convection represented by h c,ap-c and by thermal radiation represented by h r,ap-c, to the bottom plate by thermal radiation represented by h r,ap-bp (W/ m 2 K), which is the radiation heat transfer coefficient between the absorbing plate and the bottom plate, and to the fluid by convection represented by h c,ap-f (W/m 2 K), which is the

6 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 605 convection heat transfer coefficient of fluid on the absorbing plate. Hence, the energy balance on the absorbing plate requires S ( c,ap-c r,ap-c )( ap c ) r,ap-bp ( ap bp ) c,ap-f ( ap = h + h T T + h T T + h T T f ), (3) where T bp (K) is the mean temperature on the bottom plate. For the fluid, the heat gained from the absorbing plate by convection represented by h c,ap-f is distributed to the heat gain q u, which is carried away by the fluid and the thermal loss to the bottom plate by convection represented by h c,f-bp (W/m 2 K), which is the convection heat transfer coefficient of fluid on the bottom plate, resulting in the following energy balance: h ( T T ) = q + h ( T T ), (4) c,ap-f ap f u c,f-bp f bp where q u =c p m f (T fo T fi ), in which c p (J/kgmK) is the specfic heat of air and m f (kg/m 2 s) is the air mass flow rate per unit area of collector. On the bottom plate, the heat gains from the fluid via convection represented by h c,f-bp and from the absorbing plate via thermal radiation represented by h r,ap-bp are balanced by the thermal loss to the ambient via conduction represented by h b (W/m 2 K), which is the conduction heat transfer coefficient across the insulation; that is, H ( T T ) + h ( T T ) = h ( T T ). (5) r,ap-bp ap bp c,f-bp f bp b bp a With the assumption of T f = (T fi + T fo )/2, it is found from Eq. (2) that T c a I + ( h, - + h, - ) T + ( h + h, - ) T = h + h + h h c c ap c r ap c ap w r c s a c,ap-c capc, - w + r, c s (6) from Eq. (3) T ap S h h T h T h T = + (, - +, ) +, +, h + h + h + h c ap c r ap c c r ap bp bp c ap f f cap, c r,ap c r, ap bp c, ap f, (7) from Eq. (4) T f h, ( T + T ) + 2c m T = 2h + 2c m c ap f ap bp p f fi cap, f p f, (8) and from Eq. (5) T bp ht + h, T + h, T = h + h + h b a r ap bp ap c ap f f b r, ap bp c, ap f. (9)

7 606 LIU ET AL. The instantaneous efficiency of solar heat gain of the collector is q c T T c T T u pmf( fo fi) 2 pmf( f fi) h = = =. I I I Determination of Heat Transfer Coefficients The convection heat transfer coefficient from the glass cover due to wind is recommended by McAdams (1954) as hw = Vw, where V w (m/s) is the wind velocity of the ambient air and it is usually assumed that V w = 1.5 m/s (Zhai et al., 2005), giving h w = 11.4 W/m 2 K. In this paper, h w = 11.4 W/m 2 K is also used. The radiation heat transfer coefficient from the glass cover to sky referred to the ambient air temperature T a (K) may be obtained as follows (Zhai et al., 2005) (10) (11) 2 2 Tc Ts hrc, s c( Tc Ts)( Tc Ts ) ( ) = se + + ( T T ), (12) c a where σ = W/m 2 K 4 is the Stefan-Boltzmann constant, ε c is the emissivity of thermal radiation of the glass cover, and the sky temperature T s (K) is estimated by the formulation given by Swinbank (1963) T s = T 15.. (13) The radiation heat transfer coefficients between the glass cover and the absorbing plate and between the absorbing plate and the bottom plate are predicted respectively by a h rap, c 2 2 ( Tap Tc )( Tap Tc ) = s + +, 1/ e + 1/ e 1 ap c (14) h rap, bp = 2 2 s( Tap + Tbp )( Tap + Tbp ), 1/ e + 1/ e 1 ap bp (15) where ε ap and ε bp are the emissivities of thermal radiation of the absorbing plate and the bottom plate respectively. The conduction heat transfer coefficient across the insulation is estimated by h b ki =, Δ i (16)

8 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 607 where k i (W/m K) and Δ i (m) are respectively the thermal conductivity and mean thickness of the insulation. The convection heat transfer coefficient between the glass cover and the absorbing plate is k hc, ap c = Nuap c, H where k (W/m K) is the thermal conductivity of air, H c (m) is the mean gap thickness between the cover and the absorbing as sketched in Figure 1(b), and Nu ap-c is the Nusselt number for the natural convection in the channel formed by the cover and the absorbing. For the v-groove absorber as sketched in Figure 1(a), H c is calculated by H c = H c H g, where H c (m) is the distance between the top vertex of the v-groove absorber and the glass cover, as shown in Figure 1(a), and H g (m) is the height of the v-groove absorber. For both collectors, Nu ap-c can be estimated by the following correlation (Hollands et al., 1976) Nu ( ) = sin. q Ra Ra cosq cosq + Ra cosq 5830 ap c c , (17) (18) which is valid for 0 θ 75, where the + symbol in the superscript means that only positive values of the terms in the square brackets are to be used (i.e., use zero if the term is negative), θ ( ) is the angle of inclination of the collector and Ra is the Rayleigh number, which is defined as 2 3 p ap c c r cgb( T T) H Ra km, (19) in which ρ (kg/m 3 ), β (1/K) and μ (kg/m s) are the density, thermal expansion coefficient and dynamic viscosity of air, and g (m/s 2 ) is the acceleration due to gravity. The convection heat transfer coefficients for the fluid moving on the absorbing plate and on the bottom plate are calculated by k hcap, f = hcap, f = Nuap f, (20) D where Nu ap-f is the Nusselt number for the convection of fluid moving in the air flow channel, and D h (m) is the hydraulic diameter of the air flow channel formed by the absorbing and the bottom plate, which is calculated by h Dh = 2 H 3 g, (21)

9 608 LIU ET AL. for the v-groove collector and D h = 2WHg WH W + H = g W H g for the flat-plate absorber, where W (m) is the collector width and H g (m), from Figure 1(b), is 0.5 H g. For the v-groove collector, Nu ap-f can be calculated from a correlation developed by Hollands and Shewen (1991) Nu Nu Nu ap f ap ap g, (22) Hg f = Re, When Re < 2800, (23) L H g = Re + 225, when 2800 Re 10 4, (24) L H g 4 5 f = Re Re, when 10 <Re<10, (25) L where Re is the Reynolds number, which is calculated by Re = r U f D h, (26) m in which U f (m/s) is the mean velocity of fluid in the channel. For the flat-plate collector, however, Nu ap-f is estimated by the following correlation (Kays and Crawford, 1980), where 08 Nu ap-f = Re. (27) Re = 2r U f H g (28) m For T from 280 K to 470 K, the following empirical correlations can be used (Weast, 1970) to estimate the air density, thermal conductivity and dynamic viscosity, r = T T T, (29) k = ( T T ) 10, (30)

10 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS m = ( T T ) 10, (31) while constant β = 1/T (1/K) and c p 1000 J/kg K can also be assumed. Solutions of Temperatures and Efficiency It is apparent from Eq. (6) to Eq. (10) that no analytic solutions can be obtained for the temperatures T c, T ap, T bp, and T f and the efficiency η as most of the heat transfer coefficients are functions of these temperatures. Hence, the values of these parameters will be obtained numerically with an iteration method. The procedure is first using guessed temperatures to calculate the heat transfer coefficients, which are then used to estimate new temperatures, and if calculated new temperatures are larger than 0.01% of their respective guessed values then these new temperatures will be used as the guessed temperatures for the next iteration and the process will be repeated until all the newest temperatures obtained are within ±0.01% from their respective previous values. RESULTS AND DISCUSSIONS The configuration parameters for the solar air collectors considered here are W, L, H g, H c, Δ i, k i, ε ap, ε bp, ε c, α ap, α c, and τ c, and the parameters featuring the operating conditions are I, θ, m f, and T fi respectively. The parameters characterizing the thermal performance of these collectors are η, T c, T ap, T bp, and ΔT f = T fo T fi, which is the fluid temperature difference at the inlet and the outlet, h c,ap-f, h c,ap-c, h r,ap-bp, h r,ap-c, and h r,c-s respectively. In this section, solutions are first obtained under the typical configurations and operating conditions for both collectors to catch a glimpse of the general thermal performances of these collectors and the improvements achievable with the use of the v-groove absorber with respect to the flat-plate absorber. A comprehensive comparison is then followed to examine the thermal performances of these two collectors under a wide range of configurations and operating conditions. Results Under Typical Configurations and Operating Conditions The following values are used for the parameters under the typical configurations and operating conditions: I = 600 W/m 2, θ = 45, W = 1 m, L = 2 m, H g = 0.05 m, H c = 0.05 m, m f = 0.05 kg/m 2 s, T a = 300 K, T fi = 300 K, Δ i = 0.05 m, k i = W/m K, ε ap = 0.94, ε bp = 0.94, ε c = 0.9, α ap = 0.95, α c = 0.06, τ c = 0.84, and h w = 11.4 W/m 2 K. The results under the typical configurations and operating conditions are listed in Table 1. It is found that the v-groove absorber collector is considerably superior to the flat-plate absorber collector (about 18% higher efficiency), indicating that the use of the v-groove absorber does significantly improve the thermal performance of a solar air collector with respect to a flat-plate absorber, which is in line with the results of Karim and Hawlader (2006). Apparently this improvement of thermal performance is due to the enhanced convection heat transfer rate between the air and the absorber in the v-groove absorber collector, which is more than 10 times of that in the flat-plate collector, resulting

11 610 LIU ET AL. Table 1 Results under the typical configurations and operating conditions. Parameter V-groove absorber collector Flat-plate absorber collector η q u (W/m 2 ) T c (K) T ap (K) T bp (K) T fo (K) h r,c-s (W/m 2 K) h r,ap-c (W/m 2 K) h c,ap-c (W/m 2 K) h r,ap-bp (W/m 2 K) h c,ap-f (W/m 2 K) Ra Re Nu c Nu f in much smaller temperatures at the cover, at the absorber, and at the bottom plate, and larger heat gains for the fluid in the v-groove absorber collector. Results Under Various Configurations Although the configuration parameters are W, L, H g, H c, Δ i, k i, ε ap, ε bp, ε c, α ap, α c, and τ c, it is obvious that small values of α c and k i and large values of Δ i and α ap will result in higher efficiencies for both collectors. Further, it is unnecessary to analyze both the effects of L and W. Therefore, only the results for the configuration parameters L, H g, H c, ε ap, ε bp, and ε c, are presented here to show their effects on the thermal performance of the collectors. The strategy used below to analysis the effect of a specific parameter on the thermal performance of the collectors is to only change the values of this specific parameter while the values used in the typical configurations and operating conditions as presented in the previous section are used for the other parameters. Effect of L. The results showing the effect of the collector length L on the thermal performance of the collectors are presented in Figures 3 and 4, where L changes in the range of 0.5 m to 5 m. From the results, it is clearly seen that L has no effect on the thermal performance of the flat-plate collector. The effect of L on the thermal performance of the v-groove collector is observed to be negligible, although it is also observed that an increase in L will result in a monotonically small amount of reduction of both h c,ap-f and h r,c-s. Effect of H g. The results showing the effect of H g, the height of the v-groove absorber, on the thermal performance of both collectors are presented in Figures 5 and 6, where H g changes in the range of m to 0.2 m. From the results it is found that H g has a large effect on the thermal performance of both collectors. With the increase of H g, the efficiencies of both collectors decrease monotonically while the temperatures on the cover, absorber and bottom plate increase monotonically. These trends are mainly due to the monotonic reduction of the convection heat transfer from the absorber to the fluid and the monotonic increases of the thermal radiation heat losses from the absorber to the bottom plate and to the cover with the increase of H g, as shown in Figure 6. It is therefore

12 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 611 Figure 3 Results showing the effect of the collector width L on the thermal performance of both collectors. Figure 4 Results showing the effect of L on the heat transfer coefficients of both collectors.

13 612 LIU ET AL. Figure 5 Results showing the effect of the gap thickness H g between the absorber and the bottom plate on the thermal performance of both collectors. Figure 6 Results showing the effect of H g on the heat transfer coefficients of both collectors.

14 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 613 essential to use a small size of the v-groove absorber to achieve a higher collector efficiency. For the flat-plate collector, it is essential to maintain a small gap between the absorber and the bottom plate for a higher efficiency. Effect of H c. The results showing the effect of H c, the distance between the cover and the top vertex of the v-groove absorber, on the thermal performance of both collectors are presented in Figures 7 and 8, where H c changes in the range of 0.02 m to 0.2 m. From the results, it is apparent that H c has a negligible effect on the thermal performance of both collectors, although h c,ap-c decreases monotonically with the increase of H c for both collectors and h r,c-s slightly increases with the increase of H c for the v-groove collector, indicating that the heat loss through the air convection inside the channel formed by the cover and the absorber is negligible. Effect of e ap and e c. The results showing the effect of e ap, the emissivity of thermal radiation of the absorbing plate on the thermal performance of both collectors are presented in Figures 9 and 10, where e ap changes in the range of 0.01 to From the results, it is found that ε ap has a large effect on the thermal performance of both collectors, especially that of the flat-plate collector. With the increase of e ap, it is found that the efficiencies and the temperature on the absorber, as expected, decrease monotonically, while the temperatures on the cover and the bottom plate increase monotonically. The reason for these trends are apparently due to the linear increase of the thermal radiation heat losses from the absorber to the bottom plate, whereas e ap has negligible impact on the convection heat transfer from the absorber to the fluid, as shown in Figure 10. It is therefore essential to maintain the emissivity of thermal radiation on the absorber as small as possible (that is, to use a selected coating that has a very high absorptivity of solar radiation, but a quite small emissivity of thermal radiation) to achieve a higher collector efficiency, no matter that it is the v-groove absorber collector or a flat-plate collector. These observations and Figure 7 Results showing the effect of the gap thickness H c between the absorber and the glass cover on the thermal performance of both collectors.

15 614 LIU ET AL. Figure 8 Results showing the effect of H c on the heat transfer coefficients of both collectors. Figure 9 Results showing the effect of the emissivity of thermal radiation of the absorber ε ap on the thermal performance of both collectors.

16 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 615 Figure 10 Results showing the effect of ε ap on the heat transfer coefficients of both collectors. conclusions are also found to hold for ε c, which is the emissivity of thermal radiation of the glass cover. Effect of e bp. The results showing the effect of e bp, the emissivity of thermal radiation of the bottom plate on the thermal performance of both collectors are presented in Figures 11 and 12, where e bp changes in the range of 0.01 to From the results, it is found that e bp has a negligible effect on the thermal performance of the v-groove absorber collector, although the heat loss through thermal radiation from the absorber to the bottom plate increases monotonically with the increase of e bp, as shown in Figure 12(c), as expected. It is also observed that when e bp increases from 0.01 to 0.99, the efficiency of the flat-plate collector has a slight increase due to the slight decreases of the temperatures on the cover and on the absorber and large increase of the temperature on the bottom plate. It is therefore optimal to use a large value of e bp in the flat-plate collector. Results Under Various Operating Conditions As mentioned above, the parameters characterizing the operating conditions of the collectors are I, θ, m f, and T fi respectively. It was found that θ has a negligible effect on the thermal performance of both collectors. Hence, only the results for the parameters I,

17 616 LIU ET AL. Figure 11 Results showing the effect of the emissivity of thermal radiation of the bottom plate ε bp on the thermal performance of both collectors. Figure 12 Results showing the effect of ε bp on the heat transfer coefficients of both collectors.

18 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 617 m f, and T fi are presented here to show their effects on the thermal performance of the collectors. Effect of I. The results showing the effect of the solar insolation rate incident on the glass cover I on the thermal performance of both collectors are presented in Figures 13 and 14, where I changes in the range of 250 W/m 2 to 1000 W/m 2. From the results, it is apparent that the effect of I on the thermal performance of both collectors is negligible, although the temperatures on the cover, absorber and bottom plate are observed to increase monotonically with the increase of I. The increase of I is observed to linearly increase the thermal radiation heat losses from the absorber to the bottom plate and to the cover, but to monotonically reduce the thermal radiation heat loss from the cover to the sky, as shown in Figure 14. However, I has no effect on the convection heat transfer between the absorber and the fluid. Effect of 0 f. The results showing the effect of the air mass flow rate per unit area of collector m f on the thermal performance of both collectors are presented in Figures 15 and 16, where m f changes in the range of kg/m 2 s to 0.25 kg/m 2 s. From the results, it is found that m f has large effects on the thermal performance of both collectors, especially when its value is small (<0.1 kg/m 2 s). In this range, an increase of m f significantly reduces the temperatures on the cover, absorber and bottom plate as well as the thermal radiation between the absorber and the bottom plate and between the absorber and the cover as well as the convection between the absorber and the cover. However, an increase of m f also dramatically increases the convection between the absorber and the fluid and the thermal radiation between the cover and the sky. The combination of these effects results in the significant increase of the efficiency of the collectors. Nevertheless, further increase of m f beyond 0.1 kg/m 2 s does not significantly improve the thermal performance of both collectors and it is therefore recommended to maintain m f at a value above 0.1 kg/m 2 s for optimal thermal performances of both collectors. Figure 13 Results showing the effect of the solar insolation rate incident on the glass cover I on the thermal performance of both collectors.

19 618 LIU ET AL. Figure 14 Results showing the effect of I on the heat transfer coefficients of both collectors. Figure 15 Results showing the effect of the air mass flow rate per unit area of collector m f on the thermal performance of both collectors.

20 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 619 Figure 16 Results showing the effect of m f on the heat transfer coefficients of both collectors. Effect of T fi. The results showing the effect of the inlet fluid temperature T fi on the thermal performance of both collectors are presented in Figures 17 and 18, where T fi changes in the range of 295 K to 365 K. From the results, it is observed that the efficiencies of both collectors decrease dramatically and almost linearly with T fi, while the temperatures on the cover, absorber and bottom plate increase significantly and also almost linearly with T fi, indicating that T fi has large effects on the thermal performance of both collectors. However, T fi has a negligible effect on the convection heat transfer from the absorber to the fluid for both collectors, although it increases the convection heat transfer from the absorber to the cover and the thermal radiations between the absorber and the bottom plate and between the absorber and the cover. It also reduces dramatically the thermal radiation loss from the cover to the sky. Therefore, it is essential to maintain the inlet fluid temperature close to that of the ambient fluid to achieve a better thermal performance for both collectors. CONCLUSIONS A comprehensive parametric study has been carried out on the thermal performance of a v-groove absorber collector under a wide range of configurations and operating conditions. The aim of the use of the v-groove absorber is to enhance the heat transfer rate inside the air flow channel by increasing the heat transfer surface area, which will result in a better thermal performance and a high efficiency. To quantify the achievable

21 620 LIU ET AL. Figure 17 Results showing the effect of the inlet fluid temperature T fi on the thermal performance of both collectors. Figure 18 Results showing the effect of T fi on the heat transfer coefficients of both collectors.

22 A PARAMETRIC STUDY ON V-GROOVE SOLAR AIR COLLECTORS 621 improvements with the v-groove absorber, a flat-plate solar air solar air collector that has both a flat absorber and a flat bottom plate, is also considered. The results can be summarized as follows: The v-groove absorber solar air collector has a significantly superior thermal performance to that of the flat-plate one, with 18% more achievable efficiency under the typical configurations and operating conditions. To achieve better thermal performance for the collectors, it is essential to; use a small size of the v-groove absorber for the v-groove absorber collector and to maintain a small gap between the absorber and the bottom plate for the flat-plate collector; to use selected coatings that have a very high absorptivity of solar radiation, but a very small emissivity of thermal radiation on the absorber and glass cover; to maintain an air mass flow rate above 0.1 kg/m 2 s, and to operate the collectors with the inlet fluid temperature close to that of the ambient fluid. The collector length, the distance between the cover and the absorber, the solar insolation rate incident on the collectors, the inclination of the collectors, and the emissivity of thermal radiation on the bottom plate are fount to have negligible effects on the efficiencies of the collectors, although they may have significant effects on the temperatures on the cover, absorber, and bottom plate, and on the heat transfer rate between various plates and the fluid. ACKNOWLEDGMENTS The financial support from the 973 Program (2007CB216405), the New Century Excellent Talents Program in University of China (NCET ), The International Collaboration Scheme of Yunnan Province, the Natural Science Foundation of Yunnan Province (Key Projects 2003E0004Z), the National Natural Science Foundation of China ( ), and the JCU Faculty Grant Scheme is gratefully acknowledged. REFERENCES Duffie, J.A. and Beckman, W.A. (1991). Solar engineering of thermal processes, 2nd Ed. New York: John Wiley & Sons. Gao, W.F. Analysis and performance of a solar air heater with cross corrugated absorber and backplate, M. Sci. Thesis, Yunnan Normal University, China, Gao, W.F., Lin, W.X. and Lu, E.R. (2000). Numerical study on natural convection inside the channel between the flat-plate cover and sine-wave absorber of a cross-corrugated solar air heater. Energy Conversion & Management 41: Goldstein, L., Sparrow, E.M. (1976). Experiments on the transfer characteristics of a corrugated fin and tube heat exchanger configuration. ASME J. Heat Transfer 98: Goldstein, L., Sparrow, E.M. (1977). Heat/mass transfer characteristics for flow in a corrugated wall channel. ASME J. Heat Transfer 99: Hollands, K.G.T., Shewen, E.C. (1991). Optimization of flow passage geometry for air-handling plate type solar collectors. ASME J. Solar Energy Eng. 103: Hollands, K.G.T., Unny, T.E., Raithby, G.D., Konicek, L.J. (1976). Free convection heat transfer across inclined air layers. ASME J. Heat Transfer 98: Karim, M.A., Hawlader, M.N.A. (2006). Performance evaluation of a v-groove solar air collector for drying applications. Applied Thermal Eng. 26: Kays, W.M., Crawford, M.E. (1980). Convective heat and mass transfer, 2nd Ed. New York: McGraw-Hill.

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