Performance model of a novel evacuated-tube solar collector based on minichannels

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1 Available online at Solar Energy 85 (2011) Performance model of a novel evacuated-tube solar collector based on minichannels Neeraj Sharma, Gerardo Diaz School of Engineering, University of California-Merced, 5200 North Lake Rd., Merced, CA 95343, USA Received 27 January 2010; received in revised form 17 October 2010; accepted 2 February 2011 Available online 2 March 2011 Communicate by: Associate Editor G.N. Tiwari Abstract Thermal performance of a novel minichannel-based solar collector is investigated numerically. The particular collector consists of a U-shaped flat-tube absorber with a selective coating on its external surface. The working fluid flows inside an array of minichannels located in the cross-section of the absorber along its length. The absorber is enclosed in an evacuated-glass envelope to minimize convective losses. Performance and pressure drop are evaluated for different inlet temperatures and flow rates of the working fluid. Thermal performance of minichannel-based solar collector is compared to that of an evacuated tube collector without minichannels from the literature. Configurations with and without a concentrator are analyzed. Ó 2011 Elsevier Ltd. All rights reserved. Keywords: Minichannel; Solar collector; Evacuated tube 1. Introduction The growing world-wide demand and utilization of fossil fuels together with the respective increase in greenhouse gas emissions have stimulated researchers, businesses, and governments to pursue and promote research related to renewable energy sources. Solar energy is one such promising source, but its efficient conversion into a usable form continues to be a topic of active research. Thermal energy is one of the many forms in which we can transform and utilize the energy from the sun. Solar thermal systems provide the capability of generating heat, electric power, and cooling in a sustainable way for a variety of applications. A relatively large range of temperatures can be obtained with different collector configurations. For instance, flat-plate collectors can operate between 20 and 80 C, evacuated-plate collectors operate between 50 and 120 C. Non-imaging-optics based compound-parabolic Corresponding author. Tel.: address: gdiaz@ucmerced.edu (G. Diaz). concentrators or CPCs (Winston, 1974) combined with evacuated-tube collectors can operate at 200 C at efficiencies near 50% without the need of tracking. Minichannels have been successfully utilized in a variety of applications such as single-phase heat exchangers (Fernando et al., 2008), condensers and evaporators (Qi et al., 2009), fuel cell cooling applications (Yahia et al., 2007), electronics cooling, automobile cooling, and air conditioning systems (Goodremote et al., 1988). However, the use of minichannels in solar collectors has not been analyzed yet. The use of minichannels in solar collectors is motivated, firstly, by the increase in heat transfer area between tube walls and the working fluid, and secondly, by the reduction in the thermal resistance against heat conduction in the absorber since no external fin is utilized. A variety of collector and concentrator designs have been proposed and analyzed in the literature. Some of the common configurations correspond to flat-plate solar collectors (Rojas et al., 2008, 2009), CPC solar collectors (Kim et al., 2008, 1981), evacuated-tube collectors (Sawhney et al., 1987), all-glass tubular collector (Shah X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.solener

2 882 N. Sharma, G. Diaz / Solar Energy 85 (2011) Nomenclature A area (m 2 ) A 1, A 2 internal areas used in fin analysis and shown in Fig. 4 (m 2 ) A o area of the opening of the concentrator (m 2 ) C p specific heat of fluid (J/kg K) D diameter (m) d minimum wall thickness of minichannels (m) E b i blackbody emissive power at temperature T i (W/m 2 ) F i!j view factor from surface i to j F Fanning friction factor F adjacent [R,S] view factor of two plane perpendicular surfaces as defined in Appendix F parallel [P,Q] view factor of two plane parallel surfaces as defined in Appendix G incident radiation on a surface (W/m 2 ) h convective heat transfer coefficient (W/m 2 K) J surface radiosity (W/m 2 ) k thermal conductivity (W/m K) _m mass flow rate (kg/s) N number of ports Nu Nusselt number P o Poiseuille number p pressure (Pa) Q s average solar flux at Earth s surface (W/m 2 ) Q s m modified average solar flux (W/m 2 ) q 00 heat flux (W/m 2 ) R fin fin resistance (K/W) R tot absorber resistance (K/W) Re Reynolds number r radius (m) s, s 1, s 2, s 3, s 4, f 1, f 2 surfaces for calculation of view factors T temperature (K) T average temperature (K) t small gap between the absorber flat-tubes U fluid flow velocity Greek Symbols a absorptivity h angle of incidence of solar radiation D difference e emissivity g efficiency g o optical efficiency of the concentrator q reflectivity q l fluid density r Stefan oltzmann constant s transmissivity Subscripts a absorber surface without coating amb ambient c absorber surface with coating conv convective f fluid g glass inner go glass outer h hydraulic i internal in fluid inlet inf infinity m mean out fluid outlet Superscripts b blackbody s solar t thermal and Furbo, 2007), helix tube solar collector system (oonchom et al., 2007), and non-imaging-optics based CPC (Welford and Winston, 1978; Diaz and Winston, 2008) combined with dewar or absorber-fin evacuated-tube collector. The development of non-imaging-optics in the past decades has improved the optical efficiency of solar concentrators and brought it close to the thermodynamic limit. However, improvements in the thermal efficiency are still needed in order to lower the cost of power generated by solar thermal technology. Along this line of research, a novel design of minichannel-based evacuated-tube solar collector has been recently proposed (Diaz, 2008). In general, the hydraulic diameter of a minichannel tube ranges between 200 lm and 3 mm (Kandlikar et al., 2002). Thus, as the hydraulic diameter decreases, the pressure drop per unit length of the channel increases so that the optimal dimensions of the minichannel are governed by a balance between the gain in the heat transfer rate and the increase in the pressure drop. In the present work the thermal analysis of a solar collector based on minichannels is performed by developing an appropriate heat transfer model of the radiative and convective thermal exchange. In analyzing the flow of the fluid in minichannels, wall surface effects, such as electrokinetic or electroosmotic forces were neglected. 2. Geometry description The geometry of the solar collector based on minichannels is shown in Fig. 1. The working fluid enters the collector through an inlet pipe that is connected to a manifold,

3 N. Sharma, G. Diaz / Solar Energy 85 (2011) (Kreith and ohn, 2001). The following assumptions have been used: Steady-state operation is assumed. The minichannels are assumed to have a constant internal diameter and roughness. A perfect vacuum inside the glass is assumed. The effects of a concentrator have not been included (this effect is considered in Section 5). A two-band approximation is used to characterize the difference in the properties between solar and thermal radiation. All radiation and all surfaces are assumed to be diffuse. All radiation emitted by different surfaces is assumed to be thermal. Temperature variation on coated surface is assumed to be small compared to the average temperature of the coating. Radiation falling on the absorber surface is assumed to be distributed uniformly. Fig. 1. Top and side views of the minichannel-based solar collector. not shown in the figure. The inlet manifold is connected to the inlet side of the absorber tube that contains an array of minichannels, also referred to as ports, as shown in Fig. 1. The fluid flow splits in several parallel paths and continues to move through the absorber along the U-shaped configuration. A selective coating is applied to the external surface of the absorber. No external fins are used on the absorber. The working fluid exits the collector through the outlet ports into a manifold that is connected to the outlet pipe, also not shown in the figure. The inlet and outlet sections of the U-shaped absorber are separated by a small gap t to avoid thermal short circuit. The entire assembly is enclosed in an evacuated-glass tube that utilizes glass-to-metal seals to maintain the vacuum. The outer glass surface reflects a fraction of the incident solar radiation and the rest is transmitted through the glass wall. Thermal radiation is also emitted by the glass to the ambient. The energy exchange is described by Eqs. (1) and (2), where the superscripts s and t indicate solar and thermal radiation, respectively. A go G s go ¼ A goq s A go J go ¼ t g A go E b g Eb amb þ q s g A gog go þ A g G s g ss g The inner face of the glass cover experiences surface-tosurface radiation with the selective coating material on the surface of the absorber and with a portion of the absorber ð1þ ð2þ 3. Mathematical model The principles utilized to develop the thermal model of the minichannel-based solar collector are described in the following sections Radiation exchange The developed thermal model considers radiation exchange and convective heat transfer for the geometry described in Fig. 1. The radiation analysis is performed utilizing standard methodology for analysis of enclosures Fig. 2. Energy exchange at various surfaces.

4 884 N. Sharma, G. Diaz / Solar Energy 85 (2011) located inside the gap region which is not coated. This exchange involves both solar and thermal radiation. Energy exchange at various surfaces is shown in Fig. 2, where G s go is the net outer glass surface irradiation, and J go is the net outer glass surface radiosity. The exchange of solar radiation is represented by Eqs. (3) (8). It is observed that the emissive powers of the various surfaces were not included since all radiation emitted by different surfaces was assumed as thermal. A c J s c ¼ qs c A cg s c A c G s c ¼ F g!ca g J s g þ F c!ca c J s c þ F a!ca a J s a A a J s a ¼ qs a A ag s a A a G s a ¼ F g!aa g J s g þ F c!aa c J s c þ F a!aa a J s a A g J s g ¼ A goq s s s g þ qs g A gg s g A g G s g ¼ F g!ga g J s g þ F c!ga c J s c þ F a!ga a J s a ð3þ ð4þ ð5þ ð6þ ð7þ ð8þ The terms G s g ; Gs c, and Gs a correspond to the net surface solar irradiations of inner glass surface, selective coating surface, and remaining non-coated absorber surface, respectively. Equivalently, J s g, J s c, and J s a correspond to the net surface solar radiosities of the respective surfaces. F i!j corresponds to the view factor from surface i to surface j. The surfaces exchange thermal radiation according to Eqs. (9) (14). A c J t c ¼ qt c A cg t c þ t c A ce b c ð9þ A c G t c ¼ F g!ca g J t g þ F c!ca c J t c þ F a!ca a J t a ð10þ A a J t a ¼ qt a A ag t a þ t a A ae b a ð11þ A a G t a ¼ F g!aa g J t g þ F c!aa c J t c þ F a!aa a J t a ð12þ A g J t g ¼ qt g A gg t g þ t g A ge b g ð13þ A g G t g ¼ F g!ga g J t g þ F c!ga c J t c þ F a!ga a J t a ð14þ where G t g ; Gt c,andgt a are the net surface thermal irradiations of inner glass surface, selective coating surface, and remaining non-coated absorber surface, respectively. J t g ; J t c and J t a correspond to the net surface thermal radiosities of the respective surfaces View factor calculation The view factors between the different surfaces of the minichannel-based solar collector are calculated using Eqs. (15) (35). Fig. 3 shows the various surfaces considered in the calculation. The gap between the two absorber plates has three open surfaces, namely, s 1, s 2 and s 4, and three covered surfaces, namely, s 3, f 1,andf 2. Surface s is the sum of surfaces s 1, s 2, and s 4. The view factors between these surfaces are calculated to finally obtain the view factor from inner glass surface to itself, F g!g, as given by Eq. (29). F g!g is composed of the view factor related to the fraction of radiation from glass to glass that does not go through the absorber gap, F g!g1, plus the view factor of the fraction of radiation from glass to glass that goes Fig. 3. Various surfaces at the gap between the two absorber plates. s 1, s 2, and s 4 are open surfaces, and s 3, f 1, and f 2 are solid surfaces. through the gap, F g!g2. In general, the absorber gap, characterized by t, is small but the analysis has been generalized to also account for larger values of t. The view factors of two perpendicular plane surfaces having a common edge, F adjacent [R,S], and two rectangular surfaces parallel to each other, F parallel [P,Q], were used in the model and are described in the Appendix by Eqs. (51) and (52), respectively (Modest, 2003). F g!c þ F g!s þ F g!g1 ¼ 1 ð15þ A g F g!s ¼ A s F s!g ð16þ A g F g!c ¼ A c F c!g ð17þ F s!f1 þ F s!f2 þ F s!s þ F s!s3 ¼ 1 ð18þ F s!f1 ¼ F s!f2 ð19þ A s F s!f1 ¼ A s1 F s1!f 1 þ A s2 F s2!f 1 þ A s4 F s4!f 1 ð20þ A s F s!s3 ¼ A s1 F s1!s 3 þ A s2 F s2!s 3 þ A s4 F s4!s 3 ð21þ 0:5L F s1!f 1 ¼ F adjacent ; d ð22þ F s2!f 1 ¼ F s4!f 1 ¼ F adjacent 0:5L ; d ð23þ 0:5L 0:5L F s1!f 1 ¼ F s3!f 1 ¼ F adjacent ; d ð24þ d F s1!s 3 ¼ F parallel 0:5L ; ð25þ 0:5L F s2!s 3 ¼ F s4!s 3 ¼ F adjacent d ; 0:5L ð26þ d

5 0:5L F f1!f 2 ¼ F parallel d ; d ð27þ F g!g2 ¼ F g!s F s!s ð28þ F g!g ¼ F g!g1 þ F g!g2 ð29þ F g!a ¼ F g!s 2F s!f1 þ F s!s3 ð30þ F c!a ¼ F c!c ¼ 0 ð31þ F s!g ¼ F c!g ¼ 1 ð32þ A a F a!g ¼ A g F g!a ð33þ A a F a!a ¼ A s3 2F s3!f 1 þ 2Af1 F f1!f 2 þ F f1!s 3 ð34þ A f1 F f1!s 3 ¼ A s3 F s3!f 1 ð35þ N. Sharma, G. Diaz / Solar Energy 85 (2011) Fin analysis The internal section of the absorber is modeled as a series of fins and each fin is analyzed using Eqs. (36) (42) which are obtained by performing energy balance as shown in Fig. 4. d 2 T dx þ 1 da 1 dt 2 A 1 dx dx 1 h f da 2 A 1 k a dx qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi yðxþ ¼y 0 r 2 ðx 0 xþ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A 1 ¼ 2L y 0 r 2 ðx 0 xþ 2 Z x0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A 2 ¼ 2L ð1 þ y 0 ðxþ 2 Þ dx 0 Z x0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 00 conv ¼ h f L ð1 þ y 0 ðxþ 2 ÞðT T f Þ dx 0 R fin ¼ T i T f R tot ¼ 1 N q 00 conv R fin 2 þ d 22k ð a y 0 LÞ 3.4. Energy balance ðt T f Þ¼0 ð36þ ð37þ ð38þ ð39þ ð40þ ð41þ ð42þ An energy balance is performed at the glass cover, absorber surface, and minichannel walls to calculate the average glass, absorber, and fluid outlet temperatures for a given mass flow rate and fluid inlet temperature Glass cover The energy balance for the glass cover is given by Eq. (43) h i A g G s g J s g þ G t g J t g þ A go G go J go ¼ h g A g ðt g T inf Þ ð43þ where h g is the convective heat transfer coefficient for the free convection from the surface of a horizontal cylinder and is obtained using the relation h g ¼ 1:32 DT 1=4 D (Holman, 1986). Fig. 4. Energy balance at fins inside absorber tube Absorber surface The energy balance at the glass cover is given by Eq. (44) A c G s c J s c þ G t c J t c þ A a G s a J s a þ G t a J t a ¼ 1 ðt c T f Þ ð44þ R tot Fluid-absorber interface The average temperature of the fluid along the length is calculated as follows: _mc p dt f ¼ T c T f dy ð45þ R tot L y T f ¼ T c ðt c T in Þexp ð46þ _mc p R tot L Z L T f ¼ 1 T f dy ð47þ L 0 1 ¼ T c ð_mc p R tot ÞðT c T in Þ 1 exp ð48þ _mc p R tot where the total resistance, R tot, is composed of the resistances due to the wall and the fins generated by considering circular port shapes Pressure drop calculations The frictional pressure drop for the flow of a singlephase fluid over a length L inside a minichannel is obtained using Eq. (49).

6 886 N. Sharma, G. Diaz / Solar Energy 85 (2011) Table 1 Solar collector dimensions. Parameter Unit Values Selective coating thickness m Glass outer diameter m Glass inner diameter m Absorber thickness m Absorber plate width m Channel diameter m Spacing between channels m Distance between plates (t) m Length of absorber m 2 Length of glass tube m 1 Number of ports 16 Dp ¼ 2Fq lu 2 m L D h ð49þ where U m is the mean fluid flow velocity, q l is the fluid density, D h is the hydraulic diameter of the channel, and F is the Fanning friction factor which can be obtained for a fully developed laminar flow using the relation F¼ P o =Re, where P o is the Poiseuille number that for a circular section and laminar flow takes the value of 16 (Kandlikar et al., 2006) Simulation parameters The geometric dimensions of the minichannel-based solar collector analyzed in this work are listed in Table 1. The thermal resistance due to the thickness of the thin layer of selective coating was not considered in the simulation so the radiative properties of the coating have been used directly at the external and side surfaces of the absorber tube. The average values of material thermophysical properties utilized are presented in Table 2. The working fluid corresponded to Duratherm 600, where temperaturedependent properties were obtained from Duratherm (2009). The radiative properties of glass and selective coating for solar and thermal radiation are listed Table 3. A common measure of collector performance is provided by the collector efficiency, defined as the ratio of the useful energy gain over any time period to the incident solar energy over the same time period (Duffie and eckman, 1974). The performance of the minichannelbased collector is compared against the performance of an evacuated-tube collector of equivalent size but with a round-tube pipe attached to an absorber plate (Rahman et al., 1984). Table 2 Material properties. Property Unit Glass Absorber Thermal conductivity W/mK Density kg/m Specific heat J/kg K Table 3 Radiative properties a. Properties Solar Thermal Glass Coating Glass Coating Absorptivity (a) Transmissivity (s) 0.85 b Reflectivity (q) Emissivity () a Taken from Tovar Fonseca (2008). b Taken from Rahman (1981). 4. Results The performance of the minichannel-based solar collector without a concentrator is compared against the results obtained for an evacuated-tube collector with round-tube configuration analyzed by Rahman et al. (1984). To make the two cases comparable, similar dimensions and parameters have been used, such that, the absorber surfaces of the two collectors have the same area and receive same amount of solar radiation Minichannel-based solar collector The effect of the mass flow rate on the efficiency of the minichannel-based collector for different inlet temperatures is shown in Fig. 5. A relatively flat profile is obtained at different inlet temperatures for mass flow rates larger than 10 3 (kg/s) as the effect of the increase in mass flow rate is offset by the decrease in fluid outlet temperature. Thus, there is no significant gain in the performance by operating the collector at high flow rates. This behavior is beneficial in terms of reducing pressure drop without sacrificing performance significantly. The efficiency of the collector is reduced by increasing the inlet temperature of the fluid mainly due to radiative losses. Fig. 5 also shows the comparison of the efficiency of the evacuated-tube collector (Rahman et al., 1984) with respect to the minichannel-based solar collector as a function of mass flow rate for the baseline conditions given in Table 4. The increase in heat transfer area between the absorber and the working fluid and the decrease in absorber resistance of the minichannel-based collector translate into an increase in efficiency over the entire range of mass flow rates simulated. Fig. 6 shows the effect of the mass flow rate on the fluid outlet temperature for the minichannel-based collector at different inlet fluid temperatures. Similar to the efficiency plot, the results show a relatively flat profile at mass flow rates larger than 10 3 kg/s. Fig. 6 also presents the comparison of the effect of mass flow rate on fluid outlet temperature for the two collectors using the baseline conditions given in Table 4. The minichannel-based solar collector shows a much larger fluid outlet temperature at low flow rates compared to the collector from Rahman et al. (1984) mainly due to the decrease in the thermal resistance

7 N. Sharma, G. Diaz / Solar Energy 85 (2011) Efficiency (%) K 343 K 363 K 383 K 403 K 423 K 443 K Minichannel based collector at T = 308 K in Evacuated tube collector at T = 308 K (a) in Mass Flow Rate (kg/s) Fig. 5. Effect of mass flow rate on efficiency of the minichannel-based collector for different fluid inlet temperatures in comparison with the performance of evacuated-tube collector from (a) Rahman et al. (1984). Dashed and dotted lines are used for the two cases being compared. Efficiency (%) x 10 4 kg/s 1.6 x 10 3 kg/s x 10 3 kg/s 4.0 x 10 2 kg/s. 55 Minichannel based collector at m = 2.0 x 10 2 kg/s. Evacuated tube collector at m = 2.0 x 10 2 kg/s (a) ( T in T amb ) / I, (K/(W/m 2 )) Fig. 7. Effect of fluid inlet temperature on efficiency for different mass flow rates in comparison with the performance of evacuated-tube collector from (a) Rahman et al. (1984). Dashed and dotted lines are used for the two cases being compared. Table 4 aseline conditions as mentioned in Rahman et al. (1984). Parameter Unit Value Solar radiation on a surface W/m Ambient temperature K 293 Wind speed m/s 5 Fluid inlet temperature K 308 Mass flow rate kg/s 0.02 Absorber length m 2 Outer diameter of glass tube m Thermal conductivity W/mK 210 in the absorber. As the flow rate is increased, the fluid outlet temperatures of both collectors approach each other. The effect of the fluid inlet temperature on the efficiency of the minichannel-based collector is shown in Fig. 7 for different inlet mass flow rates of the working fluid. For a given mass flow rate, the efficiency of the collector decreases with the increase in the fluid inlet temperature mainly due to the increase in the radiative losses at higher temperatures. The comparison of the effect of fluid inlet temperature on collector efficiency at a fixed mass flow rate is also shown in Fig. 7 for the baseline conditions given in Table 4. As expected, both collectors show a reduction in efficiency with an increase of inlet fluid temperature. However, the minichannel-based collector presents a significant advantage specially at higher operating temperatures. The small hydraulic diameter and large contact area between tube walls and working fluid can increase pressure drop inside the minichannel-based collector to a level that offsets any gain in heat transfer. Thus, the effect of mass flow rate on pressure drop per unit of length inside the minichannels is analyzed in Fig. 8 for different fluid inlet temperatures. It is observed that due to properties of the Fluid Outlet Temperature (K) K 343 K K 383 K 403 K K 443 K 250 Minichannel based collector at T in = 308K Evacuated tube collector at T = 308K (a) in Mass Flow Rate (kg/s) Fig. 6. Effect of mass flow rate on fluid outlet temperature of the minichannel-based collector for different fluid inlet temperatures in comparison with the performance of evacuated-tube collector from (a) Rahman et al. (1984). Dashed and dotted lines are used for the two cases being compared. Pressure gradient (Pa/m) x K 363 K 403 K 443 K Mass Flow Rate (Kg/s) Fig. 8. Effect of mass flow rate on pressure drop per unit of length inside minichannels for different inlet temperatures.

8 888 N. Sharma, G. Diaz / Solar Energy 85 (2011) Pressure gradient (Pa/m) ( T in T amb ) / I, ( K/(W/m 2 )) 8.0x10 4 Kg/s 1.6x10 3 Kg/s 4.0x10 3 Kg/s 2.0x10 2 Kg/s Table 5 Parameters used in ray-tracing as mentioned in O Gallagher (2008). Parameter Unit Value Insolation W/m Ambient temperature K 293 Mass flow rate kg/s Emittance 0.12 Reflectivity of mirror surface 0.96 Geometric concentration 1.2 Ray-tracing is done with simplified geometry of the absorber as shown in Fig. 10a and b. Diffraction effects of the glass are neglected Optical efficiency of the reflectors by ray-tracing Fig. 9. Effect of inlet temperature on pressure drop per unit of length inside minichannels for different mass flow rates. working fluid, such as viscosity and density, the operation of the collector at low temperatures is not recommended. Start-up conditions in large systems might require a temporal external heating source to reduce the initial pumping power required at near-ambient temperatures. Fig. 9 displays the effect of the fluid inlet temperature on the pressure drop per unit of length inside the minichannels for different mass flow rates. High flow rates are not recommended for the operation of the collector. 5. Analysis with a concentrator A symmetric CPC reflector for a vertical-fin absorber is designed following the methodology described in O Gallagher (2008) and Welford and Winston (1978). The design consists of two tilted parabolic sections, each with their focus at the top edge of the absorber, as shown in Fig. 10a and b. The parabolic profile ends at the point, where the edge ray intersects the concentrator surface. A circular profile completes the concentrator shape from the acceptance angle to the bottom of the concentrator. The circle has its center at the top edge of the absorber O Gallagher (2008). The following assumptions were used in this analysis: (a) (b) Ray-tracing was utilized to calculate the fraction (g o )of the solar energy entering the opening of the concentrator that gets to the surface of the absorber, for two incidence angles of the solar radiation, i.e. 0 and 35. Fig. 10a and b shows three sample rays out of a total of 50,000 used for the ray-tracing. Table 5 shows the parameters used in the simulation. Using the optical efficiency for the concentrator obtained through ray-tracing, overall performance of the collector is calculated as explained in Section 3 with Q s m used in place of Qs, where Q s m is defined by Eq. (50). Q s m ¼ g oq s A o cos h ð50þ A g F g!c 5.2. Minichannel-based solar collector with the concentrator Fig. 11 shows the efficiency of the minichannel-based collector with a concentrator compared against the experimental data obtained with a comparable evacuated-tube solar collector without minichannels from the literature. Efficiency Minichannel based collector at θ = 0 o Minichannel based collector at θ = 35 o Experimental results from reference (b) Fig. 10. Cross-section profile of the CPC concentrator for the minichannel-based solar collector. Three sample rays out of 50,000 are shown for (a) h =0 and (b) h =35. Fluid Inlet Temperature ( o C) Fig. 11. Effect of inlet temperature on the efficiency of the minichannelbased collector with a concentrator for two angles of incidence of solar radiation in comparison with experimental data from reference (b) O Gallagher (2008).

9 The test data was obtained by O Gallagher (2008) with the long axis of the collector oriented in the east-west direction and the normal to the opening tilted downwards from the zenith by an angle equal to the latitude. The most common range of acceptance half-angle is ±35 (O Gallagher, 2008). The efficiency of the minichannel-based collector is calculated for the two extreme angles of incidence of the solar radiation, i.e. 0 and 35. The efficiency at 0 is lower than the efficiency at 35 mainly because of the higher gap losses at 0. The results show that with the increase in the inlet temperature, the efficiency of the collector decreases because of the increase in radiative losses due to higher temperature of the absorber surface. Comparison with the experimental results from the literature shows a distinct advantage of the minichannel-based collector in terms of efficiency at higher operating temperatures. For example, at h =0, the efficiency of the minichannel collector is within the experimental uncertainty of the test data for temperatures below 170 C, approximately. Above this temperature, the minichannel-based collector shows a higher efficiency. The results for h =35 show that the efficiency of the minichannel-based collector is always higher than the experimental efficiency obtained by O Gallagher (2008) for the evacuated-tube collector without minichannels. At this angle, the gains in thermal efficiency with respect to the highest value of the experimental data correspond to 5%, 8.7%, 10.7%, and 20.7% at inlet temperatures of 26.1 C, 97.4 C, C, and C, respectively. 6. Conclusions A numerical model of a novel minichannel-based solar collector is developed in this work. The results of the model show a gain in efficiency when compared to a similarly sized evacuated-tube solar collector, without minichannels, obtained from the literature under identical operating conditions. Analyses of the performance with and without concentrator are reported. The reduction in the heat path from the absorber surface to the working fluids benefits operation at higher temperatures. The efficiency of the minichannel-based collector with a concentrator is sensitive to the gap loss which can be reduced by further optimizing the shape near the bottom of the concentrator. Pressure drop and efficiency calculations suggest operation of the collector at mass flow rates between 10 3 and 10 2 kg/s for the geometry and operating conditions analyzed in this work. Acknowledgements The authors thank Prof. Roland Winston for his valuable suggestions for the design of the non-imaging-optics concentrator used in Section 5. Appendix A The following view factor relations have been utilized in the model and have been obtained from Modest (2003) N. Sharma, G. Diaz / Solar Energy 85 (2011) F adjacent ½R; SŠ ¼ 1 ps S 1 tan 1 S þ R 1 tan 1 R pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 2 þ S 2 tan 1 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 1 R 2 þ S 2 4 ln ð1 þ R2 Þð1 þ S 2 Þ S 2 ð1 þ R 2 þ S 2 S 2 Þ 1 þ R 2 þ S 2 ð1 þ S 2 ÞðR 2 þ S 2 Þ R2 ð1 þ R 2 þ S 2 R 2!! Þ ð51þ ð1 þ R 2 ÞðR 2 þ S 2 Þ F parallel ½P;QŠ¼ 2 ppq ln ð1 þ P 2 Þð1 þ Q 2 Þ þ P 2 þ Q 2 qffiffiffiffiffiffiffiffiffiffiffiffiffi þp 1 þ Q 2 tan 1 P pffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffi þ Q 1 þ P 2 tan 1 1 þ Q 2! pffiffiffiffiffiffiffiffiffiffiffiffi Q P tan 1 P Qtan 1 Q ð52þ 1 þ P 2 References oonchom, K., Vorasingha, A., Ketjoy, N., Souvakon, C., ongkarn, T., Performance evaluation of a helix tube solar collector system. International Journal of Energy Research 31, Diaz, G., Performance analysis and design optimization of a minichannel evacuated-tube solar collector. In: Proceedings of ASME IMECE (IMECE ). (November). 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