Abstract
The performance of a hybrid (PV/T) double–pass finned plate solar air heater (DPFPSAH) has been investigated. The air enters the collector from the upper channel and goes out the collector through the lower channel after being recycled. The studied PV module is used to produce the electrical energy needed to run the pump and blow the air into the collector. The effect of the mass flow rate of air on the outlet temperature, thermal and electrical output powers and overall efficiencies have been investigated. The DPFPSAH has been investigated with and without the PV module. Also, the effect of fins on the heater performance has been studied. The results show that the electricity produced by the PV module can run the fan and pump the air at mass flow rate lower than 0.45 kg/s. The thermal efficiency has been increased from 21% at a mass flow rate of 0.006 kg/s to 80% at a mass flow rate of 0.06 kg/s, while the electrical efficiency has been increased from 5.7% to 7.2% at the same mass flow rates.
Keywords: photovoltaic-thermal (PV/T), solar air heater, double pass, fins, efficiency.
*Corresponding Author: Tel.: +20 1226803483, E-mail address: mohammedmossad7070@gmail.com (M. M. Hegazy)
Introduction
A photovoltaic-thermal (PV/T) solar collector is a system that contains both a photovoltaic module and a solar thermal collector to be used for the production of electricity and heat simultaneously [1,2]. There are two types of (PV/T) solar collectors depending on the working medium; PV/T solar air heaters and PV/T solar water heaters. The PV/T solar air heaters have advantages over the PV/T solar water heaters, including: (i) no corrosion (ii) less leakage through joints and ducts (iii) the device is more compact, less complicated and easy to install. However, there are some disadvantages of using air as a working fluid such as the low thermal conductivity of air, so extended surfaces like fins are used to increase the surface area and to enhance the total heat transfer rate [3]. Hussain et al. [1] made an improvement of the PV/T solar collector by adding a hexagonal honeycomb heat exchanger. They have tested the system with and without the honeycomb at solar radiation of 828 W/m2 and mass flow rate ranging from 0.02 to 0.13 kg/s. They found that, at mass flow rate of 0.11 kg/s, the thermal efficiency is 27 % without the honeycomb and 87 % with the honeycomb. Ahmed et al. [4] showed that the dust affects the performance of the hybrid PV/T solar collector. They indicated that the dust decreases the thermal efficiency by 13.4 % and the highest electrical efficiency was 10.24% when the collector is clean and 5.67 % when the dust is present. Moreover, the dust decreased the total efficiency by 17.5 %. Hegazy [5] performed a comparative study on the performance of four different designs of hybrid PV/T solar air heaters namely: (Model I) in which the air flows over the absorber plate, (Model II) in which the air flows below the absorber plate, (Model III) in which the air flows over and below the absorber plate in a single pass and (Model IV) on which the air flows on both sides of the absorber with recycling. He has found that, model I has the lowest performance compared to other models which have almost the same thermal and electrical performance. Nevertheless, the Model III needs the least fan power, compared with Models IV and II. Coventry [6] studied the concentrating hybrid PV/T solar air heater. He concluded that the thermal efficiency of the concentrating PV/T system is 58 % while the electrical efficiency of this system is 11 %. This gives a total efficiency of the system as 69 %. The PV/T solar air collector with and without glass cover has been studied by Shahsavar and Ameri [7]. The results showed that the thermal efficiency increases in the presence of the glass cover while the electrical efficiency of the system decreases. Ahmed et al. [8] studied the effect of using a porous media on the performance of a hybrid PV/T solar system. The results show that the highest value of the daily thermal efficiency was 80.3% when the porous media is used.
In order to get the higher electrical efficiency, Dubey et al. [9] studied four different configuration of PV modules namely; case A:Glass to glass PV module with duct, case B: Glass to glass PV module without duct, case C: Glass to tedlar PV module with duct, case D : Glass to tedlar PV module without duct. They concluded that case A gives the highest electrical efficiency and the highest outlet temperature. The annual average electrical efficiency of the PV module in case of glass to glass type with and without duct is 10.41 % and 9.75 %, respectively. Othman et al. [10] investigated the performance of a hybrid photovoltaic/thermal (PV/T) collector consists of an array of solar cells for generating electricity, compound parabolic concentrator (CPC) to increase the radiation intensity falling on the solar cells and fins attached to the back side of the absorber plate to improve heat transfer to the flowing air. The experimental results show a good agreement with the theoretical results with a general result shows that electricity production in a PV/T hybrid module decreases with increasing temperature of the air flow. Tiwari and Sodha [11] studied the single pass PV/T solar air heater with air flow under the absorber plate, a single glass cover and a tedlar on the back of the solar cells. It was observed that the single pass glazed PV/T solar air heater without tedlar gave the higher performance.
In this paper, the PV/T double pass finned plate solar air heater (DPFPSAH) has been investigated. Rectangular fins made of galvanized iron are attached on the back surface of the absorber plate.
The aim of this work is:
To compare the performance of the double-pass finned plate solar air heater (DPFPSAH) with and without the PV module.
To calculate the daily electrical output power that is needed to run the fan and pump the air into the collector.
Effect of mass flow rate of air on various parameters such as thermal, electrical and overall efficiencies and the useful thermal and electrical output powers.
Theoretical analysis
The hybrid PV/T double-pass finned plate solar air heater is shown in Fig. (1). It consists of a glass cover, an absorber plate made of a 1m2 galvanized iron sheet with a photovoltaic module fixed on the upper surface of it. Rectangular fins are attached to the back surface of the absorber plate in order to increase the heat transfer rate. For simplicity, the energy balance equations of various elements of the system are formulated under the following assumptions: (a) The PV module is in a good contact with the absorber plate so they have the same temperature. (b) The heat capacities of the glass cover, absorber plate, and back plate are negligible. (c) The system is compact so there is no air leakage. (d) the performance of the hybrid PV/T solar air heater is steady state. (e) The flowing air temperature varies only in the direction of flow.
Depending on the previous assumptions, the energy balance equations of various elements of the PV/T (DPFPSAH) are given by:
For the glass cover:
α_g IA_g+A_g h_cg (T_fu-T_g )+A_g h_rpg (T_p-T_g )=A_g h_w (T_g-T_a )+A_g h_rgs (T_g-T_s)
(1)
For the absorber plate:
Sp =A_p h_p1 (T_p-T_fu )+A_p h_p2 ϕ(T_p-T_fl )+A_p h_rpg (T_p-T_g )+A_p h_rpb (T_p-T_b) (2)
where
Sp=A_p τ_g I [α_(p ) (1-F)+α_c F(1-η_c)] [5] (3)
η_c=0.125 [1-0.004 (T_p-293)] [5, 12] (4)
F is a packing factor that is equal to A_c⁄A_p (5)
For the back plate:
A_b h_b (T_fl-T_b )+A_b h_rpb (T_p-T_b)=A_b U_b (T_b-T_a) (6)
where (U_b=k_b/x_b) is the back conductive heat loss coefficient (W/m2 k).
For the air flowing in the upper channel:
The energy balance equation for the flowing air in the upper channel considering a unit length dx can be written as:
bdxh_p1 (T_p-T_fu )=m ̇_fu C_fu 〖dT〗_fu/dx dx+bdxh_cg (T_fu-T_g )+bdxU_S (T_fu-T_a ) (7)
where (U_s=k_s/x_s) is the side conductive heat loss coefficient (W/m2 k).
For the air flowing in the lower channel:
bdxh_p2 ϕ(T_p-T_fl )=m ̇_fl C_fl 〖dT〗_fl/dx dx+bdxh_b (T_fl-T_b )+bdxU_S (T_fl-T_a ) (8)
Where ϕ and ɳ_fin are given by the following equations [13]:
ϕ=1+(A_fin/A_p )ɳ_fin , (9)
and
ɳ_fin=tanh√(2hH⁄(k_fin t))/(2hH⁄(k_fin t)). (10)
The sky temperature T_s is calculated using Swinbank formula [14] as:
T_S=0.0552 〖T_a〗^1.5. (11)
The heat transfer coefficient due to wind h_w is calculated from the following correlation [15]:
h_w =2.8+3V (12)
where V is the wind speed (m/s).
The radiative heat transfer coefficient from the glass cover to the sky is given as[14]
h_rgs=Ɛ_g σ (〖T_g〗^2+〖T_s〗^2)(T_g+T_s). (13)
The radiative heat transfer coefficient from the absorber plate to the glass cover is calculated from the equation[14]:
h_rpg=(σ(〖T_p〗^2+ 〖T_g〗^2 )(T_p+T_g))/((1/Ɛ_p )+(1/Ɛ_g )-1) (14)
The radiative heat transfer coefficient from the absorber plate to the back plate is calculated from the equation[14]:
h_rpb=(σ(〖T_p〗^2+ 〖T_b〗^2 )(T_p+T_b))/((1/Ɛ_p )+(1/Ɛ_b )-1) (15)
The convective heat transfer coefficient h_p1from the absorber plate to the air flowing in the upper channel is assumed to be equal to the convective heat transfer coefficient from the flowing air in the upper channel to the glass coverh_cg[16].
h_p1=h_cg=(〖Nu〗_fr k_fu)/D_hu , (16)
where k_fu is the thermal conductivity (W/m K) of the air flowing in the upper channel ,〖Nu〗_fr is the Nusselt number for forced convection mode and D_hu is the hydraulic diameter (m) of the upper channel which can be calculated as [14]:
D_hu=2bd_fu / (b+d_fu) , (17)
where〖 d〗_fu is the depth of the upper flow channel.
The Nusselt number for forced convection mode 〖Nu〗_fr is given as:
For laminar flow (Re<2300) [17]:
〖Nu〗_fr=5.4+(a[Re Pr(D_h/L) ]^m)/(1+c[Re Pr(D_h/L) ]^n ) , (18)
where
Prandtl number Pr=0.7. While a, c, m and n are the empirical constants. a=0.0019, c=0.00563, m=1.71 and n=1.17.
For turbulent flow (Re>2300) [18]
〖Nu〗_fr=0.0158 〖Re〗^0.8 (19)
where Re is the Reynold's number calculated using the following correlation [21]:
Re=(2m ̇)/(μ (b+d_f)) (20)
Where μ is the dynamic viscosity (kg/m s) of the flowing air and d_f is the depth (m) of the flow channel.
It is assumed that the convective heat transfer coefficient from the absorber plate to the flowing air in the lower channel h_p2 is equal to the convective heat transfer coefficient from the flowing air in the lower channel to the back plate h_b [18] and they are calculated using the correlation given for h_p1 (Eq.16).
After some mathematical manipulation the following expressions for T_g,T_pand T_b are obtained as :
T_g=n_1+n_2 T_fu+n_3 T_fl+n_4 T_a+n_5 T_s . (21)
T_p=n_6+n_7 T_fu+n_8 T_fl+n_9 T_a+n_10 T_s . (22)
T_b=n_11+n_12 T_fu+n_13 T_fl+n_14 T_a+n_15 T_s . (23)
The values of n's coefficients in Eqs. (21, 22 and 23) are given in Appendix A
Substituting T_g, T_pand T_busing Eqs. (21), (22) and (23), Eqs.(7) and (8) become
〖dT〗_fu/dx=-A_1 T_fu+E_1 T_fl+f_1 (t). (24)
〖dT〗_fl/dx=-A_2 T_fl+E_2 T_fu+f_2 (t). (25)
Where the coefficients〖 A〗_1, A_2, E_1, E_2, f_1 (t)and f_2 (t) are given in Appendix B.
By using the elimination technique [20], Eqs. (24) and (25) are solved. Assuming f_1 (t) and f_2 (t) have average values (f_1 (t)) ̅ and (f_2 (t)) ̅ over a time interval from 0 to t and maybe considered as constants [21].
From Eq.(25) we have
T_fu=1/E_2 [ (dT_fl)/dx+A_(2 ) T_fl–(f_2 (t)) ̅]. (26)
Substituting from Eq.(26) into Eq.(24),we can get
(d^2 T_fl)/(dx^2 )+(A_1 〖+A〗_2 ) 〖dT〗_fl/dx+(A_1 A_2-E_1 E_2 ) T_fl=A_1 (f_2 (t) ) ̅+E_2 (f_1 (t)) ̅. (27)
The general solution of Eq.(27) maybe given as [22]
T_fl=T_par+〖 T〗_comp (28)
where〖 T〗_par and T_comp are the particular and the complimentary solutions, respectively.
Assuming Ω is the differential operator, then the solution of Eq.(27) is:
Ω^2+(A_1 〖+A〗_2 )Ω+(A_1 A_2-E_1 E_2 )=0 (29)
The solution of Eq.(29) is given by
Ω_█(1@2)=(-(A_1+A_2 )±√(〖〖(A〗_1+A_2)〗^2-4(A_1 A_2-E_1 E_2)))/2. (30)
And the complimentary solution T_compis given by
T_comp=C_1 e^(Ω_(1 ) X)+C_2 e^(Ω_(2 ) X), (31)
where C_1 and C_2 are constants.
The outlet temperature of the air flowing in the upper channel T_fuois equal to the inlet temperature of the air flowing in the lower channel T_fli during circulation of the flowing air in the upper channel at x=L .So the constantsC_1 and C_2 are given by
C_1=(E_2 T_fui-(Ω_2+A_2 ) T_fuo+Ω_2 T_par+(f_2 (t)) ̅)/(Ω_1-Ω_2 ). (32)
C_2=((Ω_1+A_2 ) T_fuo-E_2 T_fui-Ω_1 T_par-(f_2 (t)) ̅)/(Ω_1-Ω_2 ). (33)
T_par is assumed to be a constant because, the non-homogeneous part of Eq.(27) is a constant [22].so the particular solution is obtained as
T_par=(A_1 (f_2 (t) ) ̅+ E_2 (f_1 (t)) ̅)/(A_1 A_2-E_1 E_2 ). (34)
By substitution from Eq.(28) into Eq.(26), we get
T_fu (x)=1/E_2 [(Ω_1+A_2 ) C_1 e^(Ω_1 x)+(Ω_2+A_2 ) C_2 e^(Ω_2 x)+A_2 T_par-(f_2 (t)) ̅] . (35)
The outlet T_fuo and average T_fuav temperatures of the flowing air in the upper channel are obtained as
T_fuo=├ T_fu (x) ┤|_(x=L)
= 1/E_2 [(Ω_1+A_2 ) C_1 e^(Ω_1 L)+(Ω_2+A_2 ) C_2 e^(Ω_2 L)+A_2 T_par-(f_2 (t)) ̅] . (36)
and
T_fuav=1/L ∫_0^L▒〖T_fu (x)dx〗
=( 1/(LE_2 ))[(Ω_1+A_2 ) C_1/Ω_1 (e^(Ω_1 L)-1)+(Ω_2+A_2 ) C_2/Ω_2 (e^(Ω_2 L)-1)+A_2 LT_par- L(f_2 (t)] ) ̅ . (37)
Also the outlet T_flo and average T_flav temperatures of the air flowing in the lower channel are obtained as
T_flo=├ T_fl (x) ┤|_(x=2L)=C_1 e^(2LΩ_1 )+C_2 e^(〖2LΩ〗_2 )+T_par (38)
and
T_flav=1/2L ∫_0^2L▒〖T_fl (x)dx〗
=(1/2L)[C_1/Ω_1 (e^(2LΩ_1 )-1)+C_2/Ω_2 (e^(〖2LΩ〗_2 )-1)+2LT_par ]. (39)
2.1. Parameters affecting the performance of the hybrid PV/T double pass finned plate solar air heater (DPFPSAH):-
A computer program was developed to solve the energy balance equations in order to study the factors affecting the performance of the hybrid solar collector, which include temperature distribution, electrical, thermal, and electro-hydraulic efficiencies and also pumping, electrical and thermal powers.
The total thermal output power is given by [23]
Q ̇_u=m ̇_f C_f (T_flo-T_fui). (40)
The electrical output power of the PV/T solar air heater is given by[5]
Q ̇_p=η_c α_c 〖τ_g〗^2 FA_p I . (41)
The instantaneous thermal efficiency η_Tis given as [24]
η_T=Q ̇_u/(IA_p ) . (42)
The daily thermal efficiency η_(T-d)of the system is given as
η_(T-d)=(m ̇_f C_f ∑▒〖(T_flo-T_fui)〗)/(A_P ∑▒I). (43)
The electrical efficiency of the PV/T air heater is given as [24]:
η_E=Q ̇_p/(A_c I) . (44)
We cannot calculate the total efficiency by adding both the thermal and electrical efficiencies; and therefore, the efficiency conversion factor C_f given by Joshi et al. [25] could be used to calculate the total efficiency with higher accuracy and its value in the most PV/T solar air heaters is taken to be between 0.35 and 0.40. In the present work, the value of C_fis taken to be 0.38.
Therefore, the overall efficiency of PV/T air heater is given by [25]:
η_(overall )=η_E/C_f +η_T . (45)
The fan needs an electrical energy to blow the air into the heater, thus we can assume that the efficiencies of the fan and the motor are 70 % and 90 %, respectively [23].Then the fan power P_fan and the flow pumping power P_flow can be calculated as [23]:
P_fan=P_flow/(η_fan η_motor), (46)
P_flow=m ̇ΔP/ρ, (47)
Where m ̇ and ρ are the mass flow rate (kg/s) and the density (kg/m3) of the flowing air, respectively.
The total pressure drop ΔP (N/m2) can be expressed as the sum of the pressure drop through the upper and lower channel ΔP_ch and the dynamic loss due to duct joints ΔP_joints[26].
ΔP=ΔP_ch+ΔP_joints , (48)
where
ΔP_ch=2ρfV^2 L/D_h , (49)
ΔP_joints=ΚρV^2/2 , (50)
and
V=m ̇/(ρbd_f). (51) The coefficient has the value of 2.2 as in a previous study [27].
The friction factor f for the smooth channel is given by [28]
f=16/Re , for laminar flow (52)
= 0.059〖Re〗^(-0.2) for turbulent flow (53)
The friction factor f for the finned channel is given by [29]
f=24/Re , for laminar flow (54)
= 0.079〖Re〗^(-0.25) for turbulent flow (55)
If we assume that about 30 % of the electrical energy is lost in the charge regulator, inverter and cabling system then only 70 % of this energy is stored in the batteries so the useful electrical power is only 56 % [5].
Hence Q ̇_useful=0.56Q ̇_p . (56)
The net available electrical power is given by:
Q ̇_(NET )=0.56Q ̇_p-P_fan . (57)
The electro-hydraulic efficiency of the PV/T solar collector can be calculated as [5]
η_(e-h)=Q ̇_NET/(F I A_P) . (58)
Method of numerical calculations
Energy balance equations for different elements of the hybrid PV/T double- pass finned plate solar air heater are solved using a suitable computer program. The climate data are taken for Tanta in a summer day (13/6/2015). Temperatures of the glass cover, PV module, absorber plate, and the flowing air are initially guessed. The temperature of the inlet air is assumed to be equal to the ambient temperature. Using the initial temperatures, all internal and external heat transfer coefficients were calculated and used for calculating the temperatures of various elements of the system. The steps were repeated with the new values of the different heat transfer coefficients until all temperatures were calculated along the 24 hour. The thermal and electrical powers as well as thermal, electrical and overall efficiencies were then calculated. The Various thermo-physical parameters used in the calculation have been summarized in Table 1.
4. Results and discussions
4.1. Temperature distribution of different elements of the system
Figures 2 A and B show the hourly variations of the calculated temperatures of different elements of the hybrid PV/T solar air heater using the data of solar radiation and ambient temperature measured at 13/6/2015 when ( m) ̇_fu=m ̇_fl=0.02 kg/s, L=b=1 m, A_c=0.5 m^2, d_fu=d_fl=0.08 m and x_b=x_s=0.05 m. From Fig. 2.A, it is clear that the solar radiation intensity increases with time and reaches its maximum value of 930 W/m2 at 2.0 pm. Also it is shown that the maximum values of T_fuav, T_flav and 〖 T〗_flo are found to be 35.5, 47, and 56oC, respectively. The average temperature of the air flowing in the lower channel T_flav is higher than that of flowing in the upper channel and this is due to circulation and fins. Fig. 2.B shows that the maximum values of T_g, T_b are 49 oC and 47 oC, respectively. The highest temperature of the absorber plate equals 93 oC.
4.2. Effect of the PV module on the DPFPSAH performance
Figure 3 presents the maximum outlet temperature T_(flo,max) of the collector with and without the PV module versus the mass flow rate m ̇. It is evident that in both cases, T_(flo,max) decreases with increasing( m) ̇ because the heat capacity of air increases with the mass flow rate. Figure 3 also shows that T_(flo,max) in case of the collector without the PV module is higher than when using the PV module due to the reduction in the collector area with the PV module. The results indicate that the PV module decreases the outlet temperature T_flo by an average value of 21 %.
Figure 4 introduces a comparison between the daily thermal output power ( Q) ̇_(u,daily) of the DPFPSAH with and without the PV module. It is clear that ( Q) ̇_(u,daily) of the collector without the PV module is higher than that of the collector with the PV module due to the higher outlet temperature T_flo of the collector without the PV module compared to that of the collector with the PV module.( Q) ̇_(u,daily) increases with increasing ( m) ̇ until a typical value of 0.26 kg/s beyond which the increase becomes insignificant for both systems. For the DPFPSAH without the PV module, ( Q) ̇_(u,daily) is found to be increased from 3629 to 6735 Wh/day with increasing the mass flow rate from 0.01 to 0.26 kg/s. Whereas it is increased from 6735 to 6773 Wh/day with increasing ( m) ̇ from 0.26 to 0.34 kg/s. For the DPFPSAH with the PV module, it is found that, ( Q) ̇_(u,daily) increases from 2064 to 5425 Wh/day with mass flow rate ranges from 0.01 to 0.26 kg/s, and is increased from 5425 to 5471 Wh/day when( m) ̇ is increased from 0.26 to 0.34 kg/s. On the other hand, Fig. 4 also presents the variation of the daily electrical output power ( Q) ̇_(p,daily) with the mass flow rate m ̇. It is found that ( Q) ̇_(p,daily) increases with increasing m ̇ until 0.18 kg/s then the increase becomes trivial. ( Q) ̇_(p,daily) is found to increase from 221 to 276 Wh/day when m ̇ is raised from 0.01 to 0.18 kg/s but with m ̇ ranges from 0.18 to 0.34 kg/s, ( Q) ̇_(p,daily) is only increased from 276 to 282 Wh/day.
Figure 5 shows the thermal efficiency η_T of the collector with and without the PV module at different values of the mass flow rate( m) ̇. It is obvious that η_T increases with increasing( m) ̇ due to the decreased collector temperature with increasing( m) ̇. Fig.5 also indicates that η_T in case of the collector without the PV module is higher than that of the collector with the PV module due to the higher ( Q) ̇_u of the collector without the PV module compared to that of the collector with the PV module. The PV module decreases the thermal efficiency by about 34%. The decrease in the thermal efficiency will be compensated in generating the electrical power in order to operate the fan and pump the air into the collector.
Figure 6 presents the variations of thermal, electrical and overall efficiencies of the hybrid PV/T solar air heater with different values of the mass flow rate. It is shown that with increasing( m) ̇, all efficiencies are increased. It is also clear that η_T is increased from 21 % at ( m) ̇=0.006 kg/s to 80 % at ( m) ̇=0.06 kg/s, while η_E is increased from 5.7 % at mass flow rate of 0.006 kg/s to 7.2 % at ( m) ̇=0.06 kg/s. Then〖 η〗_overall is increased from 36 % to 98 % at the same mass flow rates.
4.3. Effect of fins on the performance of the hybrid PV/T solar air heater
In order to get higher electrical efficiency, the PV module has to be maintained at a low temperature, so the fins are used to reduce the temperature of the absorber plate by increasing its heat capacity and consequently the temperature of the PV module decreases, then the electrical efficiency is increased. Also fins are used to increase the heat transfer rate in order to get higher outlet temperature T_flo.
Variations of the absorber plate temperature T_p of the hybrid PV/T solar air heater at different values of ( m) ̇ with and without fins are presented in Fig.7. It is evident that the fins reduce T_p as a result of increasing of its heat capacity. By decreasing the temperature of the PV module the electrical efficiency is increased as in Fig.8 where 〖 η〗_E is increased by 5.7% due to the presence of the fins. It is also shown from the figure that, fins increase the thermal efficiency by about 9%. Similar results are obtained by Kumar and Rosen [30].
4.4. Effect of the mass flow rate on fan and module powers
Figure 9 shows the variation of the daily fan ( P_(fan,daily)) and module (( Q) ̇_(p,daily)) powers with different values of the mass flow rate( m) ̇. It is clear that this type of hybrid PV/T solar air heaters could provide the electrical power needed to run the fan and pump the air into the collector until ( m) ̇ reaches 0.45 kg/s beyond which the power of the fan exceeds the power of the module. Thus, it is advisable to use this system with mass flow rate equals or lower than 0.45 kg/s.
Variations of the electro-hydraulic efficiency of the PV/T solar air heater with the mass flow rate are shown in Fig.10. It is evident that, at mass flow rates (less than 0.2 kg/s), the electro-hydraulic efficiency is almost constant, but with increasing the mass flow rate, the electro-hydraulic efficiency takes a steep downward path and this is due to the requirement of the fan power increases with increasing the mass flow rate, and according to Eqs.(54) and (55), when the power of the fan exceeds net power, the electro-hydraulic efficiency decreases sharply. This result shows a good agreement with Hegazy [5].
4.5. Effect of the packing factor (A_c⁄A_p )
Figure 11 presents the effect of the packing factor on the thermal, electrical and overall efficiencies. It is evident that as the packing factor increases, the electrical efficiency increases due to the increased area of the module. As the packing factor increases, the thermal efficiency decreases because the surface area of the collector is decreased. The figure shows that as the packing factor increases from 0.16 to 1, the overall efficiency decreases from 70 to 65%.
Conclusion
On the basis of the results obtained after studying the performance of the hybrid PV/T solar air heater and investigating the effect of the PV module and the addition of fins, we conclude the following:
The PV module can produce electricity and run the pump to below the air into the collector until the mass flow rate reaches 0.45kg/s beyond which the power of the fan goes over the power of the module, so we cannot perform this type of PV/T solar air heaters at a mass flow rate higher than 0.45 kg/s.
The outlet temperature T_flo is decreased by an average value of 21% in the presence of the PV module.
The addition of fins increases the thermal and electrical efficiencies by about 9% and 5.7%, respectively.
The electro-hydraulic efficiency is being stable at a mass flow rate less than 0.2 kg/s but at higher mass flow rates it takes a steep downward path.