Recycle Effect on Device Performance of Wire Mesh Packed Double-Pass Solar Air Heaters

Abstract

A new device for inserting an absorber plate to divide a flat-plate channel into two subchannels to conduct double-pass wire mesh packed operations was developed. The proposed wire mesh packed device improves the heat transfer efficiency substantially as compared that to flat-plate single-pass and double-pass operations using the same working dimensions, and the improvement of device performance was investigated experimentally and theoretically. Good agreement between the theoretical prediction and the measured values from the experimental results was achieved. Considerable heat transfer improvement was obtained employing wire mesh packed double-pass operations under the absorber plate with external recycle. The influences of recycle ratio on the heat transfer efficiency and the power consumption increase were also discussed.

1. Introduction

Low temperature energy technology solar collectors are a special kind of heat exchanger that transforms solar radiation energy into internal energy of the working fluids flowing through the heat exchanger devices. Solar radiation collection by solar collectors has attracted a great deal of interest in recent years, and these devices are widely used, mostly for heating both water and air fluids. Solar air collectors are less complicated and easy to implement coupled with existing space heating and drying systems [1], drying agricultural products [2,3] and some industrial applications [4,5]. The underside of the absorber plate and the edge of casing are well insulated to reduce conduction losses while the transparent covers on the top are used to reduce convection losses.

In addition to the effects of forced convection [6] and free convection [7,8], a considerable improvement on collector performance is achievable by increasing the heat-transfer area and creating air turbulence inside the flow ducts by using extended heat-transfer areas [9], air turbulence [10] and packing materials [11,12]. The higher convective heat-transfer coefficient and higher thermal energy efficiency are achieved in the solar collector of the present recycling device as the wire mesh is inserted in the lower channel under the absorber plate. Experimental and theoretical researches are undergoing simultaneously to design and modify the augmentation of double-pass solar air heaters [13,14,15]. Thanks to the packing wire mesh in the duct of solar air heaters for enhancing the thermal performance, the impacts of artificial turbulence were investigated in several papers [16,17,18,19], where the friction loss due to the packing wire mesh was studied as well. Thus, Kolb et al. [20] concluded that the presence of packing wire mesh in a flowing duct not only enhances both the convective heat transfer coefficient and the collector efficiency, but also increases the relatively small friction losses as compared to the conventional open channel [21]. Moreover, the forced convection enhancement due to the recycle-effect application in double-pass operations has been reported in numerous heat- and mass-transfer problems such as loop reactors [22], air-lift reactors [23], draft-tube bubble columns [24] and thermal diffusion columns [25], resulting in improved device performance. In the present work, a new double-pass solar air heater configuration that is actually the extension of the previous work [26], is studied theoretically and experimentally by adding packing wire mesh into the lower subchannel under recycling operation. An attempt has been made in the present study to: (a) provide a brief outline of both theoretical predictions and experimental results in the a wire mesh packed double-pass solar air heater; (b) discuss the exaggeration of the device performance of the effects of recycle ratio and wire mesh packing; and (c) examine the economic considerations regarding both heat-transfer efficiency improvement and power consumption increase.

2. Mathematical Modeling

Consider a recycling double-pass solar air heater with inserting an absorber plate to divide a parallel conduit with height H, length L, and width W, as shown in Figure 1.

Figure 1. A schematic drawing of a wire mesh packed double-pass solar air heater.

Figure 1. A schematic drawing of a wire mesh packed double-pass solar air heater.

The energy-flow diagram for a finite system element used for making an energy balance equation is presented in Figure 2. Before entering the lower subchannel in a double-pass device, the airflow (with air mass flow rate $\dot{m}$ and inlet temperature T_in) will mix with the recycling airflow $R\dot{m}$ and T_b,0 exiting from the upper subchannel. A conventional blower situated at the beginning of the lower channel controls the recycling air mass flow rate. The following assumptions were made in this analysis: (1) the temperatures of the absorbing plate, bottom plate and bulk fluid are functions of the flow direction only; (2) both the glass covers and fluids do not absorb radiant energy; (3) the radiant energy absorbed by the glass cover 2 (outer cover) is assumed to be negligible; and (4) all outside surfaces of the solar air collector, except the glass cover, are well insulated thermally. With the above assumptions the energy equations may be written as indicated.

Figure 2. The energy balance on energy flow within a finite fluid element.

Figure 2. The energy balance on energy flow within a finite fluid element.

2.1. Temperature Distributions on Wire Mesh Packed Solar Air Heaters

The temperature distributions of both upper and lower subchannels can be obtained by solving the energy balance equations for the absorber plate, glass cover, airflow and bottom plate. By following the similar mathematical treatment performed in our previous work [26], two simultaneous ordinary differential equation were obtained providing energy balances for the glass cover, absorber plate, bottom plate and both upper and lower subchannels, and rearranging with some algebraic equation manipulations as follows:

$$\frac{\text{d}\left(T_{\text{b}}\left(\text{ξ}\right)-T_{\text{s}}\right)}{\text{dξ}}=B_1\left[T_{\text{b}}\left(\text{ξ}\right)-T_{\text{s}}\right]+B_2\left[T_{\text{a}}\left(\text{ξ}\right)-T_{\text{s}}\right]+B_3$$

(1)

$$\frac{\text{d}\left(T_{\text{a}}\left(\text{ξ}\right)-T_{\text{s}}\right)}{\text{dξ}}=B_4\left[T_{\text{b}}\left(\text{ξ}\right)-T_{\text{s}}\right]+B_5\left[T_{\text{a}}\left(\text{ξ}\right)-T_{\text{s}}\right]+B_6$$

(2)

and thus, we get the analytical solutions of the temperature distributions of the flowing air in both lower and upper subchannels:

$$T_{\text{a}}\left(\text{ξ}\right)=k_1{e}^{Y_1\text{ξ}}+k_2{e}^{Y_2\text{ξ}}+\frac{B_3{B}_4-B_1{B}_6}{B_1{B}_5-B_2{B}_4}$$

(3)

$$T_{\text{b}}\left(\text{ξ}\right)=\frac{Y_1-B_5}{B_4}{k}_1{e}^{Y_1\text{ξ}}+\frac{Y_2-B_5}{B_4}{k}_2{e}^{Y_2\text{ξ}}+\frac{B_2{B}_6-B_3{B}_5}{B_1{B}_5-B_2{B}_4}$$

(4)

The definitions of B_i and Y_i are described in the Appendix, and the constants k₁ and k₂ in Equations (3) and (4) were determined with the use of the following boundary conditions:

$$\text{ξ}=0\text{, }{T}_{\text{a}}(0)=T_{\text{a},0}^0=\frac{T_{\text{in}}+R{T}_{\text{b}}(0)}{1+R}$$

(5)

$$\text{ξ}=1\text{, }$$

(6)

2.2. Heat Transfer Coefficients of Wire Mesh Packing

The equivalent hydraulic diameter D_e,a and D_e,b of both subchannels in double-pass devices and D_e,0 in the single-pass one, respectively, can be expressed by the characteristic length in the present devices:

$$D_{\text{e,a}}=4r_{\text{h}}=\frac{P{d}_{\text{W}}}{1-P}$$

(7)

which the hydraulic radius r_h for the lower subchannel of wire mesh packing conduit was defined by Varshney and Saini [27], and the porosity P of the wire screen matrix was defined by Chang [28]:

$$P=1-\left(\frac{n\text{π}{d}_{\text{w}}^2}{2P_{\text{t}}D}\right){\left(1+\frac{d_{\text{w}}^{\text{2}}}{P_{\text{t}}^2}\right)}^{1/2}$$

(8)

The correlated equations for the upper subchannel were derived from Kays [29] and Heaton et al. [30] for turbulent flow and laminar flow, respectively, as follows:

$$N{u}_{\text{b}}=0.0158{{\mathrm{Re}}_{\text{b}}}^{0.8}\text{[}1+{\left(D_{\text{e,b}}/L\right)}^{0.7}\text{], for turbulent flow}$$

(9)

$$N{u}_{\text{b}}=4.4+\frac{0.00398{\text{(}0.7{\mathrm{Re}}_{\text{b}}{D}_{\text{e,b}}/L\text{)}}^{1.66}}{1+0.0114{\text{(}0.7{\mathrm{Re}}_{\text{b}}{D}_{\text{e,b}}/L\text{)}}^{1.12}}\text{, for laminar flow}$$

(10)

and the estimation equation for the wire mesh conduit was developed by Saini and Saini [31]:

$$\begin{array}{c}N{u}_{\text{a}}=\frac{h_{\text{a}}{\text{D}}_{\text{e,a}}}{k}=4.0\times {10}^{-4}{\text{(}{\mathrm{Re}}_{\text{a}}\text{)}}^{1.22}{\text{(}\frac{P_{\text{t}}}{D_{\text{e,a}}}\text{)}}^{0.625}{\text{(}\frac{s}{10P_{\text{t}}}\text{)}}^{2.22}{\text{(}\frac{l}{10P_{\text{t}}}\text{)}}^{2.66}\\ \times \exp [-1.25{(\ln \frac{s}{10P_{\text{t}}})}^2]\exp [-0.824{(\ln \frac{l}{10P_{\text{t}}})}^2]\text{, }{\mathrm{Re}}_{\text{a}}>1800\end{array}$$

(11)

2.3. Heat Transfer Coefficients and Collector Efficiency Improvement

The total heat loss coefficient was estimated from the solar air collector to the surroundings is the summation of top, edge and bottom loss rate, i.e.,

$$U_{\text{L}}=\left\{U_{\text{T}}{A}_{\text{c}}(T_{\text{p,m}}-T_{\text{s}})+U_{\text{B}}{A}_{\text{c}}(T_{\text{R,m}}-T_{\text{s}})+U_{\text{E}}{A}_{\text{E}}[(T_{\text{a,m}}-T_{\text{s}})+(T_{\text{b,m}}-T_{\text{s}})]\right\}/A_{\text{c}}(T_{\text{p,m}}-T_{\text{s}})$$

(12)

An empirical equation of U_T was developed [32] following the basic procedure [33] for the horizontal collector with two glass covers, as shown in Figure 1, in which the edge U_E and bottom U_B loss coefficients depend mostly on the insulation thickness by conduction. Moreover, the thermal resistance from the inner glass cover to the ambient air may be calculated with the aid of the heat-transfer coefficient for free convection of air between two glass covers by using Hottel’s empirical equation [33]. The convective heat-transfer coefficient for air flowing over the surface of outer glass cover was calculated using the following empirical equation given by McAdams [34]:

$$h_{\text{w}}=2.8+3.0V$$

(13)

The outlet temperature of T_b,0 can be calculated from Equation (7) with ξ = 0:

$$T_{\text{b}}\left(0\right)=T_{\text{b,0}}=\frac{Y_1-B_5}{B_4}{k}_1+\frac{Y_2-B_5}{B_4}{k}_2+\frac{B_2{B}_6-B_3{B}_5}{B_1{B}_5-B_2{B}_4}$$

(14)

The useful energy gained by the flowing air was calculated from the following relation once the inlet and outlet temperatures are determined:

$$Q_{\text{u}}=M_{\text{a}}{A}_{\text{c}}\text{(}{T}_{\text{a,L}}-T_{\text{a,0}}^{\text{0}}\text{)}+M_{\text{b}}{A}_{\text{c}}\text{(}{T}_{\text{b,0}}-T_{\text{b,L}}\text{) }$$

(15)

The collector efficiency η_W of a wire mesh packed solar air heater that relates the actual useful energy gain from the incident solar radiation was defined by plugging Equation (12) into Equation (16) as follows:

$${\text{η}}_{\text{W}}=Q_{\text{u}}/A_{\text{c}}{I}_0={\text{τ}}_{\text{g}}^{\text{2}}{\text{α}}_{\text{p}}-U_{\text{L}}\text{(}{T}_{\text{p,m}}-T_{\text{s}}\text{)}/I_0=\dot{m}{C}_{\text{p}}\text{(}{T}_{\text{b,0}}-T_{\text{in}}\text{)}/A_{\text{c}}{I}_0=\left[-M_{\text{b}}/I_0\left(1+R\right)\right]\text{(}{T}_{\text{b,}0}-T_{\text{in}}\text{)}$$

(16)

Therefore, the average temperatures of the absorbing plate are readily obtained by rearranging Equation (16) as follows:

$$T_{\text{p,m}}=T_{\text{s}}+\left[I_0{\text{α}}_{\text{p}}{\text{τ}}_{\text{g}}^{\text{2}}-\frac{M_{\text{b}}}{\text{1}+R}(T_{\text{b,0}}-T_{\text{in}})/U_{\text{L}}\right]$$

(17)

The collector efficiency improvements, I_F and I_W, employing both flat-plate and wire mesh packed solar air heaters, respectively, are defined by the percentage increase in the collector efficiency related to a single-pass device under the same operating conditions as follows:

$$I_{\text{F}}=\frac{{\text{η}}_{\text{F}}-{\text{η}}_{\text{S}}}{{\text{η}}_{\text{S}}}\times 100\%$$

(18)

$$I_{\text{W}}=\frac{{\eta }_{\text{W}}-{\eta }_{\text{S}}}{{\eta }_{\text{S}}}\times 100\%$$

(19)

in which η_F, η_W and η_S, respectively, denote the collector efficiency in flat-plate type and wire mesh packed double-pass and downward-type single-pass solar air heaters.

The following are the system properties, operating conditions and essential physical properties employed in this study, as represented in Table 1. The method for theoretical prediction of collector efficiencies in the present study is similar to that developed in our previous work [26], except for the alternative configuration of the flow pattern. An initial value of η_W is calculated from Equation (16) coupled with the use of all appropriate equations for the given collector geometries, physical properties and operating conditions, once the average temperatures T_a,m, T_b,m and T_p,m are specified. The new guessed average temperatures T_a,m, T_b,m and T_p,m are then re-calculated using Equations (3), (4) and (17), respectively, with the iteration calculations until tolerance is small enough (say less than 1 × 10⁻³). After the accurate outlet air temperature of Equation (14) is obtained, the corresponding value of the collector efficiency η_W is thus obtained in Equation (16).

Table 1. Specifications of system properties, operating conditions and essential physical properties.

Parameters		Operation parameters		Physical properties
Ac (m2)	0.09	$\dot{m}$ (kg/s)	0.0107, 0.0161, 0.0214	αP	0.96
H (m)	0.05	Tin (°C)	20, 30, 40	εσ	0.94
L (m)	0.3	Ts (°C)	20 ± 0.1	εP	0.8
W (m)	0.3	I0 (W/m2)	830 ± 20, 1100 ± 20	εR	0.94
l (m)	0.015	V (m/s)	1.0	τσ	0.875
–		–		ks (W/m·K)	0.033

Table 1. Specifications of system properties, operating conditions and essential physical properties.

Parameters		Operation parameters		Physical properties
Ac (m2)	0.09	$\dot{m}$ (kg/s)	0.0107, 0.0161, 0.0214	αP	0.96
H (m)	0.05	Tin (°C)	20, 30, 40	εσ	0.94
L (m)	0.3	Ts (°C)	20 ± 0.1	εP	0.8
W (m)	0.3	I0 (W/m2)	830 ± 20, 1100 ± 20	εR	0.94
l (m)	0.015	V (m/s)	1.0	τσ	0.875
–		–		ks (W/m·K)	0.033

3. Experimental Procedure

A 0.3 m long and 0.3 m wide wire mesh packed double-pass solar air heater with external recycle was constructed of stainless steel and insulated using Styrofoam. Each flow channel was 0.05 m in height and the distance between the two glasses was 0.05 m. The collector consists of two glass covers, a black absorber plate, 20 pieces of mesh wire were welded underneath the absorber plate and perpendicular to air flowing direction with mesh interval of 0.015 m. A schematic diagram of an artificial simulation of a solar air heater is shown in Figure 3.

Figure 3. Experimental setup of a wire mesh packed double-pass solar air heater.

Figure 3. Experimental setup of a wire mesh packed double-pass solar air heater.

The ambient temperature (T_s = (30 ± 0.1) °C) was controlled by using an air conditioner and measured at a position 0.15 m above the outer glass cover. A fan provided an ambient steady airflow wind of 1.0 m/s (EUPA TSK-F1426, 14" EUPA, Xiamen, Fujian, China) in the experimental runs. The air temperatures at the inlet and outlet of the solar collector and the temperature of the absorber plate were measured with thermocouples (TFC-305A, Hwa Tai Technology Co, Ltd., Taipei, Taiwan). The ambient air was steadily supplied by a blower (Teco 3 Phase Induction Motor, Model BL model 552, Redmond Co., Owosso, MI, USA) and the flow rate was controlled by a transformer, while the flow rate was measured by an anemometer (Model 24-611, Kanomax Japan Inc. Osaka, Japan). Before entering the lower subchannel, the airflow with mass flow rate $\dot{m}$ and temperature T_in will premix the air flow exiting from the upper subchannel with $R\dot{m}$ and T_b,0 which is regulated by means of a valve situated at the end of the lower subchannel. One set of adjustable radiation sources consisted of 14 electrical energy supplies (110 V, 125 W) and was employed by using a set of on/off switches. The simulating incident solar radiation I₀ were measured and recorded with a Model No. 455 pyranometer (TSI Inc., St. Paul, Shoreview, MN, USA).

4. Results and Discussion

Both qualitative and quantitative agreements are achieved between theoretical and experimental results, as indicated in Figure 4 and Table 2 for flat-plate and wire mesh packed solar air heaters with incident solar radiation, air mass flow rate and recycle ratio as parameters.

Figure 4. Effect of the recycle ratio on collector efficiency in flat-plate and wire mesh packed solar air heaters with recycle.

Figure 4. Effect of the recycle ratio on collector efficiency in flat-plate and wire mesh packed solar air heaters with recycle.

The collector efficiency improvement increases with increasing recycle ratio and air mass flow rate in a more remarkable extent due to the convective heat-transfer coefficient enhancement by enlarging the fluid velocity. The accuracy of the theoretical predictions by measuring the deviation from the experimental results was estimated using the following definition as:

$$E=\frac{1}{N_{\exp }}{\displaystyle \sum _{i=1}^{N_{\exp }}\frac{\left|{\eta }_{\text{theo},i}-{\eta }_{\exp ,i}\right|}{{\eta }_{\text{theo},i}}}\times 100\%$$

(20)

where N_exp, η_theo,i and η_exp,i are the number of experimental runs, theoretical prediction and experimental results of collector efficiencies, respectively.

Table 2. Theoretical predictions of heat transfer efficiency of η_F and η_W.

$\dot{m}$ (kg/s)	R	I0 = 830 (W/m2)		I0 = 1100 (W/m2)
		Flat-plate	Wire mesh	Flat-plate	Wire mesh
		ηF	ηW	ηF	ηW
0.0107	0.5	0.415	0.525	0.417	0.527
	1	0.450	0.560	0.452	0.562
	1.5	0.476	0.586	0.478	0.588
	2	0.497	0.607	0.498	0.608
0.0161	0.5	0.468	0.578	0.470	0.580
	1	0.502	0.612	0.503	0.613
	1.5	0.526	0.636	0.527	0.637
	2	0.544	0.654	0.545	0.655
0.0214	0.5	0.504	0.614	0.506	0.616
	1	0.535	0.645	0.537	0.647
	1.5	0.558	0.668	0.558	0.668
	2	0.574	0.684	0.575	0.685

Table 2. Theoretical predictions of heat transfer efficiency of η_F and η_W.

$\dot{m}$ (kg/s)	R	I0 = 830 (W/m2)		I0 = 1100 (W/m2)
		Flat-plate	Wire mesh	Flat-plate	Wire mesh
		ηF	ηW	ηF	ηW
0.0107	0.5	0.415	0.525	0.417	0.527
	1	0.450	0.560	0.452	0.562
	1.5	0.476	0.586	0.478	0.588
	2	0.497	0.607	0.498	0.608
0.0161	0.5	0.468	0.578	0.470	0.580
	1	0.502	0.612	0.503	0.613
	1.5	0.526	0.636	0.527	0.637
	2	0.544	0.654	0.545	0.655
0.0214	0.5	0.504	0.614	0.506	0.616
	1	0.535	0.645	0.537	0.647
	1.5	0.558	0.668	0.558	0.668
	2	0.574	0.684	0.575	0.685

The accuracy deviations are showed in Table 3 with two incident solar radiation I₀ for both configurations with and without attaching wire mesh, respectively.

Table 3. The deviation of the experimental results from theoretical predictions both in flat-plate type and wire mesh packed.

Accuracy	$E=\frac{1}{N_{\text{exp}}}{\displaystyle \sum _{i=1}^{N_{\text{exp}}}\frac{\left|{\eta }_{\text{theo},i}-{\eta }_{\text{exp},i}\right|}{{\eta }_{\text{theo},i}}}\times 100\%$
	Flat-plate		Wire mesh
$\dot{m}$ (kg/s)	830	I0 (W/m2) 1100	830	1100
0.0107	1.58	5.38	4.27	0.85
0.0161	5.09	5.92	9.44	5.15
0.0214	2.50	3.56	6.64	5.75

Table 3. The deviation of the experimental results from theoretical predictions both in flat-plate type and wire mesh packed.

Accuracy	$E=\frac{1}{N_{\text{exp}}}{\displaystyle \sum _{i=1}^{N_{\text{exp}}}\frac{\left|{\eta }_{\text{theo},i}-{\eta }_{\text{exp},i}\right|}{{\eta }_{\text{theo},i}}}\times 100\%$
	Flat-plate		Wire mesh
$\dot{m}$ (kg/s)	830	I0 (W/m2) 1100	830	1100
0.0107	1.58	5.38	4.27	0.85
0.0161	5.09	5.92	9.44	5.15
0.0214	2.50	3.56	6.64	5.75

The agreement between the experimental results and theoretical predictions is fairly good with the error analysis of $1.58\times {10}^{-2}\le E\le 5.92\times {10}^{-2}$ and $8.50\times {10}^{-3}\le E\le 9.44\times {10}^{-2}$ for flat-plate and wire mesh packed devices, respectively, as shown in Table 3.

The theoretical and experimental results indicate that both collector efficiencies, η_F and η_W, increase with increasing recycle ratio and mass flow rate owing to the fluid velocity enlargement with enhancing the convective heat-transfer coefficient. Moreover, the theoretical predictions of I_F and I_W for the flat-plate and wire mesh packed double-pass devices, respectively, under various incident solar radiation, air mass flow rate and recycle ratio are presented in Table 4. The collector efficiency improvement, as shown in Table 4, is helpful in examining how collector efficiency improves with various operating parameters and design types. With this comparison, the advantage of the present device for all air mass flow rates, especially with $\dot{m}$ = 0.0107 kg/s and R = 2 are 96.32% and 94.32%, respectively, for I₀ = 830 and I₀ = 1100 W/m².

Table 4. Theoretical predictions of heat-transfer efficiency improvement of I_F and I_W.

m (kg/s)	R	I0 = 830 (W/m2)		I0 = 1100 (W/m2)
		Flat-plate	Wire mesh	Flat-plate	Wire mesh
		IF (%)	IW (%)	IF (%)	IW (%)
0.0107	0.5	34.19	69.79	35.44	70.60
	1	45.62	81.22	46.77	77.29
	1.5	54.11	89.71	55.15	86.96
	2	60.72	96.32	61.68	94.32
0.0161	0.5	26.56	56.29	27.44	57.25
	1	35.58	65.31	36.36	66.17
	1.5	42.11	71.84	42.80	72.61
	2	47.10	76.83	47.73	77.54
0.0214	0.5	21.79	48.36	23.97	50.94
	1	29.33	55.90	31.51	58.47
	1.5	34.69	61.26	36.86	63.83
	2	38.73	65.30	40.91	67.87

Table 4. Theoretical predictions of heat-transfer efficiency improvement of I_F and I_W.

m (kg/s)	R	I0 = 830 (W/m2)		I0 = 1100 (W/m2)
		Flat-plate	Wire mesh	Flat-plate	Wire mesh
		IF (%)	IW (%)	IF (%)	IW (%)
0.0107	0.5	34.19	69.79	35.44	70.60
	1	45.62	81.22	46.77	77.29
	1.5	54.11	89.71	55.15	86.96
	2	60.72	96.32	61.68	94.32
0.0161	0.5	26.56	56.29	27.44	57.25
	1	35.58	65.31	36.36	66.17
	1.5	42.11	71.84	42.80	72.61
	2	47.10	76.83	47.73	77.54
0.0214	0.5	21.79	48.36	23.97	50.94
	1	29.33	55.90	31.51	58.47
	1.5	34.69	61.26	36.86	63.83
	2	38.73	65.30	40.91	67.87

The influence of the inlet air temperature on the collector efficiency improvement is shown in Figure 5. The collector efficiency improvement increases with decreasing inlet air temperature. A double-pass solar air collector without recycle means R = 0 in the schematic drawing of a wire mesh packed double-pass solar air heater of Figure 1, and the theoretical predictions were also represented in Figure 5 for various inlet air temperatures. A device performance improvement is achieved in the present study as compared to a double-pass solar air collector without recycle, as indicated in Figure 5.

Figure 5. Effect of the inlet air temperature on collector efficiency in wire mesh packed solar air heaters with recycle (I₀ = 830 W/m²).

Figure 5. Effect of the inlet air temperature on collector efficiency in wire mesh packed solar air heaters with recycle (I₀ = 830 W/m²).

The present work is actually the extension previous work [26] except the recycle configuration. Figure 6 illustrates some theoretical predictions and experimental results obtained from [26] with the same design and operating parameters used in Figure 4 for comparison of the collector efficiency improvement. Further, both collector efficiencies, η_F and η_W, obtained in both devices increase with the air mass flow rate $\dot{m}$ as a parameter, however, the increment in the present device was rather sensitive. This is because the larger amount of air flow, say $\dot{m}\text{(}1+R\text{)}$, in the present device was heated in the upper subchannel and the extent of the higher improvement in the collector efficiency was achieved due to the desirable effect of the forced convection coefficient enhancement.

Figure 6. Comparisons of collector efficiency between the present and previous work [26]. Copyright 2013 Elsevier.

Figure 6. Comparisons of collector efficiency between the present and previous work [26]. Copyright 2013 Elsevier.

The power consumptions for the flat-plate, wire mesh packed and single-pass solar air heaters, respectively, may be estimated using empirical correlations as follows:

$$H_{\text{S}}=\dot{m}\ell w_{\text{f,s}}=\frac{2f_{\text{F,S}}{\overline{v}}^{2}L}{D_{\text{e,S}}}$$

(21)

$$H_{\text{D},i}=\dot{m}\left(1+R\right)\ell w_{\text{f,a}}+\dot{m}(1+R)\ell w_{\text{f,b}}=\dot{m}\left(1+R\right)\frac{2f_{\text{F,a}}{\overline{v}}^{2}L}{D_{\text{e,a}}}+\dot{m}(1+R)\frac{2f_{\text{F,b}}{\overline{v}}^{2}L}{D_{\text{e,b}}}$$

(22)

in which:

$$f_{\text{F,a}}=\text{3.5722}\times {\left(\text{1/}nP\right)}^{\text{1.0431}}{\left(P_{\text{t}}\text{/}{d}_{\text{w}}\right)}^{\text{1.1507}}{\mathrm{Re}}_{\text{a}}^{-0.43}\text{ , for }{\mathrm{Re}}_{\text{a}}>1\text{9}00\text{, for wire mesh device [35]}$$

(23)

$$f_{\text{F},i}=\frac{\text{24}}{\mathrm{Re}}\text{ , for }\mathrm{Re}<2100\text{, }i=a,b,S\text{, for flat-plate device [36]}$$

(24)

$$f_{\text{F},i}=\frac{\text{0.0791}}{{\mathrm{Re}}^{0.25}}\text{ , for 2100}<\mathrm{Re}<100,000\text{ , }i=a,b,S\text{, for flat-plate device [36]}$$

(25)

The calculated results of hydraulic dissipated energy in a single-pass device are H_S = 1.8 × 10⁻⁴, 5.72 × 10⁻⁴ and 1.25 × 10⁻³, W for $\dot{m}$ = 0.0107, 0.0161 and 0.0214 kg/s, respectively. The power consumption increments for flat-plate and wire mesh packed devices, I_P,W and I_P,F, respectively, are defined as compared to that in the downward single-pass operation:

$$I_{\text{P,W}}=\frac{H_{\text{D,W}}-H_{\text{S}}}{H_{\text{S}}}\text{ for solar air heaters with wire mesh packed}$$

(26)

$$I_{\text{P,F}}=\frac{H_{\text{D,F}}-H_{\text{S}}}{H_{\text{S}}}\text{ for flat-plate double-pass solar air heater}$$

(27)

The hydraulic dissipated power consumption energy in operating both flat-plate type and wire mesh packed double-pass solar air heaters with external recycle are investigated with mass flow rate and recycle ratio as parameters, as shown in Table 5. The theoretical results show that the hydraulic dissipated energy increases with increasing mass flow rate and recycle ratio. An economic consideration of device performance is examined by evaluating both collector efficiency improvement and power consumption increment, I_W/I_P,W and I_F/I_P,F, respectively, as illustrated in Figure 7. The effects of various recycle ratio and mass flow rate on I_W/I_P,W and I_F/I_P,F are presented graphically in Figure 7 for both flat-plate and wire mesh packed double-pass solar air heaters. These results reveal that an optimum operating condition exists between 0.5 and 1.0 for both flat-plate and wire mesh packed solar air heaters with various air mass flow rates and recycle ratios. Actually, there exists an economic selection in operating double-pass wire mesh packed solar air heaters at the optimal recycle ratio for the maximum value of I_W/I_P,W, which considers both the energy gain and energy consumption for making a good economic sense to achieve device operation profitability. Restated, the results confirm that the application of packing wire mesh to design a double-pass solar air heater is technically and economically feasible.

Table 5. The power consumption with recycle ratio and air mass flow rate as parameters.

R	Wire Mesh Packed (HD,W)			Flat-Plate Type (HD,F)
	$\dot{m}$ (kg/s)			$\dot{m}$ (kg/s)
	0.0107	0.0161	0.0214	0.0107	0.0161	0.0214
0.25	1.76 × 10−2	5.05 × 10−2	1.05 × 10−1	7.44 × 10−4	2.29 × 10−3	5.01 × 10−3
0.50	1.96 × 10−2	5.61 × 10−2	1.17 × 10−1	8.53 × 10−4	2.62 × 10−3	5.74 × 10−3
0.75	2.14 × 10−2	6.13 × 10−2	1.28 × 10−1	9.58 × 10−4	2.95 × 10−3	6.44 × 10−3
1.00	2.31× 10−2	6.62 × 10−2	1.38 × 10−1	1.06 × 10−3	3.26 × 10−3	7.12 × 10−3
1.25	2.47× 10−2	7.08 × 10−2	1.47 × 10−1	1.16 × 10−3	3.56 × 10−3	7.78 × 10−3
1.50	2.63× 10−2	7.52 × 10−2	1.57 × 10−1	1.25 × 10−3	3.85 × 10−3	8.42 × 10−3
1.75	2.78× 10−2	7.95 × 10−2	1.65 × 10−1	1.34 × 10−3	4.13 × 10−3	9.04 × 10−3
2.00	2.92× 10−2	8.35 × 10−2	1.74 × 10−1	1.43 × 10−3	4.41 × 10−3	9.65 × 10−3

Table 5. The power consumption with recycle ratio and air mass flow rate as parameters.

R	Wire Mesh Packed (HD,W)			Flat-Plate Type (HD,F)
	$\dot{m}$ (kg/s)			$\dot{m}$ (kg/s)
	0.0107	0.0161	0.0214	0.0107	0.0161	0.0214
0.25	1.76 × 10−2	5.05 × 10−2	1.05 × 10−1	7.44 × 10−4	2.29 × 10−3	5.01 × 10−3
0.50	1.96 × 10−2	5.61 × 10−2	1.17 × 10−1	8.53 × 10−4	2.62 × 10−3	5.74 × 10−3
0.75	2.14 × 10−2	6.13 × 10−2	1.28 × 10−1	9.58 × 10−4	2.95 × 10−3	6.44 × 10−3
1.00	2.31× 10−2	6.62 × 10−2	1.38 × 10−1	1.06 × 10−3	3.26 × 10−3	7.12 × 10−3
1.25	2.47× 10−2	7.08 × 10−2	1.47 × 10−1	1.16 × 10−3	3.56 × 10−3	7.78 × 10−3
1.50	2.63× 10−2	7.52 × 10−2	1.57 × 10−1	1.25 × 10−3	3.85 × 10−3	8.42 × 10−3
1.75	2.78× 10−2	7.95 × 10−2	1.65 × 10−1	1.34 × 10−3	4.13 × 10−3	9.04 × 10−3
2.00	2.92× 10−2	8.35 × 10−2	1.74 × 10−1	1.43 × 10−3	4.41 × 10−3	9.65 × 10−3

Figure 7. The values of I_W/I_P,W and I_F/I_P,F vs. recycle ratio with air mass flow rate as a parameter.

Figure 7. The values of I_W/I_P,W and I_F/I_P,F vs. recycle ratio with air mass flow rate as a parameter.

5. Conclusions

This study provides an alternative design for wire mesh packed solar air heaters with recycling operations. Significant improvements on the heat transfer efficiency are achieved by application of the recycle-effect concept to solar air heaters to conduct recycling double-pass operations. Recently, numerous papers have proposed exergy and energy analyses [37,38] to understand the effect of embedding a porous medium inside solar air heaters. The energy efficiency obtained in the case of an air mass flow rate of 0.02 kg/s is 0.5 in Figure 3 of [38], while at the air mass flow rate of 0.0214 kg/s and T_in = 30 °C in the present study, the value of collector efficiency is 0.52 with R = 0 in Figure 5. The agreement of both results achieved by embedding a porous medium and inserting a wire mesh, respectively, is pretty good. The device performance of wire mesh double-pass solar air heaters with external recycle was investigated theoretically and experimentally with the aim of making economic sense with consideration of the hydraulic dissipated energy. Meanwhile, theoretical predictions of the collector efficiency as well as the ratio of efficiency improvement and power consumption increment, say I_W/I_P,W, in recycling wire mesh double-pass solar air heaters were carried out and calculated with air mass flow rate and recycle ratio as parameters. The results show that the wire mesh packed solar air heater is economically feasible to improve the collector efficiency under recycling operation due to the promotion of turbulence intensity. This work indicates that a suitable selection of operating conditions for the new design of recycling wire mesh packed solar air heater could enhance collector efficiency with a reasonable hydraulic dissipated energy increase.