# Performance Study of Solar Air Heater Having Absorber Plate with Half-Perforated Baffles

Authors: B. K. Maheshwari; Rajendra Karwa; S. K. Gharai
Journal: ISRN Renewable Energy
 (2011)

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## Abstract

The paper presents a detailed mathematical model for performance prediction of a smooth duct solar air heater validated against the experimental results. Experimental study on a solar air heater having absorber plate with half-perforated baffles on the air flow side shows thermal efficiency enhancement of 28%–45% over that of the smooth duct solar air heater, which is attributed to the heat transfer enhancement (of the order of 180%–235%) due to the perforated baffles attached to the absorber plate and reduction in the mean temperature of the absorber plate by 20°C–25°C as compared to the temperature of absorber plate of smooth duct air heater. Using the mathematical model, the performance plot for the baffled duct air heater has been presented, and the effect of the variation of ambient parameters on the predicted thermal efficiency has been studied.


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## Body

## 1. Introduction

Flat plate collectors have been used to deliver heated air for space heating, crop drying, and similar applications requiring air at low-to-medium temperature (slightly above the ambient to about 100°C). The thermal efficiency of a smooth duct flat plate solar air hater is lower than that of a solar water heater because of a low value of heat transfer coefficient between the absorber plate and the air flowing through the collector duct. This leads to a high operating temperature of the collector, especially the absorber plate, resulting in greater heat loss from the collector. Hence, the researchers have directed their efforts towards enhancement of heat transfer coefficient by creating turbulence near the heat transferring surface using artificial roughness in various forms, such as solid roughness elements of various shapes and in different arrangements and perforated or detached roughness elements [1–18].The solid roughness elements have been shown to significantly enhance the heat transfer coefficient, but the associated increase in the friction factor is of serious concern. Further, hot zones develop in the wake of these roughness elements because of a recirculating flow in the wake region. The detached elements or elements with perforations allow a part of the flow to pass through the perforations or gap, and thus, the adverse effects of the hot zone and form drag are reduced [12–18]. Hwang and Liou in [14] studied the effect of the half-perforated turbulence promoters symmetrically mounted on two opposite walls on the heat transfer and friction in a rectangular channel. They found that the half-perforated turbulence promoters with perforations on the lower half of the ribs performed better than those with the solid type or fully perforated promoters.In the transitional flow regime (Re≤10000), which is of interest in the solar air heaters, the resistance to the heat transfer extends up to the buffer layer between the laminar sublayer and turbulent core. Hence, elements projecting beyond the sublayer, such as baffles, may be useful. To enhance the heat transfer in an asymmetrically heated rectangular section duct, Karwa et al. [17] employed solid and fully perforated baffles attached to the uniformly heated broad wall of the duct. Karwa and Maheshwari [18] carried out an experimental study of heat transfer and friction in such ducts with fully perforated (open area ratio of 46.8%) or half-perforated baffles (open area ratio of 26%) at pitch to baffle height ratio of 7.2–28.8 and flow Reynolds number of 2700 to 11150. The study showed an enhancement of 79%–169% and 133%–274% in the Nusselt number over the smooth duct for the fully perforated and half-perforated baffles, respectively, while the friction factor values are reported to be 2.98–8.02 and 4.42–17.5 times of that for the smooth duct, respectively. They found that the half-perforated baffles at a pitch to baffle height ratio of 7.2 provided the greatest performance advantage of 51%–75% over a smooth duct at equal pumping power.Since the boundary conditions in the studies of Karwa and coauthors [17, 18] correspond closely to those found in solar air heaters, the objective of the present experimental study has been to study the effectiveness of the half-perforated baffles in the solar air heater duct in the thermal performance enhancement. Half-perforated baffles of Karwa and Maheshwari [18], as shown in Figure 1, have been used with the absorber plate of the baffled duct air heater. A mathematical model for the performance prediction of the smooth duct solar air heater is also to be presented and validated against the experimental results for such air heater so that the same can be used for the performance prediction of smooth or baffled duct air heaters under a range of operating conditions.Solar air heater with perforated baffles.
(a)
A half-perforated baffle(b)
Longitudinal section of the solar air heater


## 2. Mathematical Model for Performance Prediction

Karwa and Chauhan [19] have presented a detailed nonlinear mathematical model for a smooth duct solar air heater. The model calculates the useful heat gain from the iterative solution of basic heat transfer equations of top loss and equates the same with the convective heat transfer from the absorber plate to the air using proper heat transfer correlations for the smooth duct air heater. The back loss from the collector is calculated from the iterative solution of the heat balance equation for the back surface, while the edge loss is estimated from the equation suggested by Klein [20].Figure2 shows the schematic diagram of a solar air heater. The heat balance on the air heater gives the distribution of incident solar radiation I into useful heat gain Q and the heat loss QL. The useful heat gain or heat collection rate can be expressed as
(1)Q=AI(τα)-QL=A[I(τα)-UL(Tp-Ta)],
whereAis the area of the absorber plate, (τα) is the transmittance-absorptance product of the glass cover-absorber plate combination. The heat loss QL from the collector is a sum of the losses from top Qt, back Qb and edge Qe of the collector as depicted in Figure 2.Figure 2
Heat balance on a solar air heater.The factorUL in (1) is termed as overall loss coefficient and is defined as
(2)UL=QL[A(Tp-Ta)],
where Tp is the mean absorber plate temperature and Ta is the ambient temperature.The collected heat is transferred to the air flowing through the air heater duct. Thus,(3)Q=mcp(To-Ti)=GAcp(To-Ti),
where m is the air flow rate through the collector duct and G(=m/A) is flow rate of air per unit area of the absorber plate.From the heat transfer consideration, the heat gain is(4)Q=hA(Tp-Tm),
where Tm is the mean temperature of air in the solar air heater duct and h is the heat transfer coefficient.


### 2.1. Top Loss

The heat loss from the collector glass cover, termed as top lossQt, is calculated from the iterative solution of the basic heat transfer equations given below.Heat transfer from absorber plate at a mean temperatureTp to the inner surface of the glass at temperature Tgi takes place by radiation and convection. Hence,(5)Qtpg=A[σ(Tp4-Tgi4)(1εp+1εg-1)-1+hpg(Tp-Tgi)(1εp+1εg-1)-1(1εp+1εg-1)(Tp4-Tgi4)],
where εp andεg are the emissivity of the absorber plate and the glass cover, respectively, and hpg is the convection heat transfer coefficient.The conduction heat transfer through the glass cover of thicknessδg is given by(6)Qtg=kgA(Tgi-Tgo)δg,
where kg is the thermal conductivity of the glass and Tgo is temperature of the outer surface of the glass.From the outer surface of the glass cover, the heat is rejected by radiation to the sky at temperatureTs and by convection to the ambient. Hence,(7)Qtgo=A[σεg(Tgo4-Ts4)+hw(Tgo-Ta)],
where hw is termed as wind heat transfer coefficient. It can be considered to be about 5–10 Wm−2K−1 (corresponding to the no wind to the usually encountered maximum wind velocity in the western part of Rajasthan, India). The sky temperature Ts is a function of many parameters. Some studies assume the sky temperature to be equal to the ambient temperature, because it is difficult to make a correct estimate of it, while others estimate it using different correlations.In the equilibrium,(8)Qtpg=Qtg=Qtgo=Qt.To estimate of the convective heat transfer coefficient between the absorber plate and glass coverhpg, the following three-region correlation of Buchberg et al. [21] has been used:(9a)Nu=1+1.446(1-1708Ra′)+for1708≤Ra′≤5900(+bracketgoestozerowhennegative),(9b)Nu=0.229(Ra′)0.252for5900<Ra′≤9.23×104,(9c)Nu=0.157(Ra′)0.285for9.23×104<Ra′≤106, where Ra′(=Racosβ) is Rayleigh number for the inclined air layers between the absorber plate and glass cover (collector slopeβ=0° for horizontal). The Rayleigh number is given by (10)Ra=GrPr=[g(Tp-Tgi)δpg3(Tmpgνmpg2)]Pr,
where δpg = gap between the absorber plate and glass cover, Tmpg is the mean temperature of the air in the gap, and νmpg is the kinematic viscosity of the air at Tmpg.


### 2.2. Back and Edge Losses

The back loss from the collector, refer to Figure2, is calculated from the following equation(11a)Qb=A(Tb-Ta)(δ/ki+1/hw),
where δ is the insulation thickness, ki is the thermal conductivity of the insulating material and Tb is the temperature of the bottom surface of the collector duct, which has been estimated from the iterative solution of the heat balance equation detailed below.Heat transfer by radiation from the heated absorber plate to the duct bottom surfaceQpb is calculated from(11b)Qpb=σ(Tp4-Tb4)(1εpi+1εb-1)-1.The heat flows from the heated bottom surface to the surroundings through the back insulation and to the air flowing through the duct at mean temperatureTm; that is,(11c)Qba=(Tb-Ta)(δ/ki+1/hw)+h(Tb-Tm).The absorber plate inner surface and duct bottom surface long wave emissivity valuesεpi andεb in (11b) have been assumed to be 0.9. The heat balance for the surface gives Qpb=Qba.For the estimate of the edge loss, the empirical equation suggested by Klein [20] has been used, which is(12)Qe=0.5Ae(Tp-Ta),
where Ae is the area of the edge of the air heater rejecting heat to the surroundings.Knowing the useful heat gainQ, the outlet air temperature is calculated from(13)To=Ti+Q(mcp).The thermal efficiencyη of the solar air heater is the ratio of the useful heat gain Q and the incident solar radiation I on the collector plane; that is,(14)η=Q(IA).Niles et al. [22] used the following equations to calculate the outlet air and mean plate temperatures when the solar air heater operates in open loop mode (i.e., Ti=Ta):(15a)To=Ta+I(τα)ξUL,(15b)Tp=Ti+[I(τα)UL](1-GξcpUL),where ξ=1-exp[-UL/(Gcp)(1+UL/h)-1]=(FRUL/Gcp). Parameter FR is termed as heat removal factor and is given by
(16)FR=(GcpUL)[1-exp⁡(-F′ULGcp)],
where F′ is termed as efficiency factor. It is given by(17)F′=(1+ULh)-1.The mean air temperature equation in terms of heat removal factorFR and efficiency factor F′ is(18)Tm=Ti+[Q(AULFR)]×(1-FRF′).The accuracy of the results of the performance analysis strongly depends on the use of appropriate heat transfer and friction factor correlations for the solar air heater ducts.For the asymmetrically heated high aspect ratio rectangular ducts of smooth duct solar air heater, Karwa et al. [8] used the following correlation of Ebadian and Dong [23, Equations (5.206) and (5.207)] for the apparent friction factor in the laminar regime, which takes account of the increased friction in the entrance region of the duct (19)fapp=24Re+(0.64+(38/Re))Dh(4L).The heat transfer correlation from Hollands and Shewen [24] for the thermally developing laminar flow for the smooth duct is(20)Nu=5.385+0.148Re(HL)forRe<2550.The friction factor correlation of Bhatti and Shah [25] for the transition to turbulent flow regime in rectangular cross-section smooth duct (0≤H/W≤1) is(21)f=(1.0875-0.1125HW)fo,
where(22)fo=0.0054+2.3×10-8Re1.5for2100≤Re≤3550,fo=1.28×10-3+0.1143Re-0.311for3550<Re≤107.They report an uncertainty of ±5% in the predicted friction factors from the above correlation.Considering the entrance region effect, the apparent friction factor in the turbulent flow regime is determined from the following relation for flat parallel plate duct [25]:(23)fapp=f+0.0175(DhL).The Nusselt number correlations for the transition and turbulent flow regimes in the rectangular solar air heater duct from Hollands and Shewen [24] are(24a)Nu=4.4×10-4Re1.2+9.37Re0.471(HL)for2550≤Re≤104(transitionflow)(24b)Nu=0.03Re0.74+0.788Re0.74(HL)for104<Re≤105(earlyturbulentflow).An uncertainty of an order of 5%-6% in the predicted Nusselt number can be expected [8]. As suggested by Karwa et al. [8], the laminar regime has been assumed up to Re=2800.The pressure loss and pumping power are calculated from(25)δp=[(4fappL)2ρDh](mWH)2P=(mρ)δp.The thermophysical properties of the air have been taken at the corresponding mean temperatureTm or Tmpg from the following relations of thermophysical properties, obtained by correlating data from NBS (U.S.) [26]:(26)cp=1006(Tm293)0.0155,k=0.0257(Tm293)0.86,μ=1.81×10-5(Tm293)0.735,ρ=1.204(293Tm),Pr=μcpk.Equations (1) to (26) constitute a nonlinear model for the solar air heater that has been used for the computation of the useful heat gain, thermal efficiency, and pumping power. The model has been solved by following an iterative process as depicted in Figure 3. For the heat collection estimate, the iteration was terminated when the successive values of the plate and mean air temperatures differed by less than 0.05 K. The iteration for the estimate of top loss has been continued till the heat loss estimates from the absorber plate to the glass cover and glass cover to the ambient; that is, Qtpg and Qtgo differed by less than 0.2%.Figure 3
Flow chart for iterative solution of mathematical model.


## 2.1. Top Loss

The heat loss from the collector glass cover, termed as top lossQt, is calculated from the iterative solution of the basic heat transfer equations given below.Heat transfer from absorber plate at a mean temperatureTp to the inner surface of the glass at temperature Tgi takes place by radiation and convection. Hence,(5)Qtpg=A[σ(Tp4-Tgi4)(1εp+1εg-1)-1+hpg(Tp-Tgi)(1εp+1εg-1)-1(1εp+1εg-1)(Tp4-Tgi4)],
where εp andεg are the emissivity of the absorber plate and the glass cover, respectively, and hpg is the convection heat transfer coefficient.The conduction heat transfer through the glass cover of thicknessδg is given by(6)Qtg=kgA(Tgi-Tgo)δg,
where kg is the thermal conductivity of the glass and Tgo is temperature of the outer surface of the glass.From the outer surface of the glass cover, the heat is rejected by radiation to the sky at temperatureTs and by convection to the ambient. Hence,(7)Qtgo=A[σεg(Tgo4-Ts4)+hw(Tgo-Ta)],
where hw is termed as wind heat transfer coefficient. It can be considered to be about 5–10 Wm−2K−1 (corresponding to the no wind to the usually encountered maximum wind velocity in the western part of Rajasthan, India). The sky temperature Ts is a function of many parameters. Some studies assume the sky temperature to be equal to the ambient temperature, because it is difficult to make a correct estimate of it, while others estimate it using different correlations.In the equilibrium,(8)Qtpg=Qtg=Qtgo=Qt.To estimate of the convective heat transfer coefficient between the absorber plate and glass coverhpg, the following three-region correlation of Buchberg et al. [21] has been used:(9a)Nu=1+1.446(1-1708Ra′)+for1708≤Ra′≤5900(+bracketgoestozerowhennegative),(9b)Nu=0.229(Ra′)0.252for5900<Ra′≤9.23×104,(9c)Nu=0.157(Ra′)0.285for9.23×104<Ra′≤106, where Ra′(=Racosβ) is Rayleigh number for the inclined air layers between the absorber plate and glass cover (collector slopeβ=0° for horizontal). The Rayleigh number is given by (10)Ra=GrPr=[g(Tp-Tgi)δpg3(Tmpgνmpg2)]Pr,
where δpg = gap between the absorber plate and glass cover, Tmpg is the mean temperature of the air in the gap, and νmpg is the kinematic viscosity of the air at Tmpg.


## 2.2. Back and Edge Losses

The back loss from the collector, refer to Figure2, is calculated from the following equation(11a)Qb=A(Tb-Ta)(δ/ki+1/hw),
where δ is the insulation thickness, ki is the thermal conductivity of the insulating material and Tb is the temperature of the bottom surface of the collector duct, which has been estimated from the iterative solution of the heat balance equation detailed below.Heat transfer by radiation from the heated absorber plate to the duct bottom surfaceQpb is calculated from(11b)Qpb=σ(Tp4-Tb4)(1εpi+1εb-1)-1.The heat flows from the heated bottom surface to the surroundings through the back insulation and to the air flowing through the duct at mean temperatureTm; that is,(11c)Qba=(Tb-Ta)(δ/ki+1/hw)+h(Tb-Tm).The absorber plate inner surface and duct bottom surface long wave emissivity valuesεpi andεb in (11b) have been assumed to be 0.9. The heat balance for the surface gives Qpb=Qba.For the estimate of the edge loss, the empirical equation suggested by Klein [20] has been used, which is(12)Qe=0.5Ae(Tp-Ta),
where Ae is the area of the edge of the air heater rejecting heat to the surroundings.Knowing the useful heat gainQ, the outlet air temperature is calculated from(13)To=Ti+Q(mcp).The thermal efficiencyη of the solar air heater is the ratio of the useful heat gain Q and the incident solar radiation I on the collector plane; that is,(14)η=Q(IA).Niles et al. [22] used the following equations to calculate the outlet air and mean plate temperatures when the solar air heater operates in open loop mode (i.e., Ti=Ta):(15a)To=Ta+I(τα)ξUL,(15b)Tp=Ti+[I(τα)UL](1-GξcpUL),where ξ=1-exp[-UL/(Gcp)(1+UL/h)-1]=(FRUL/Gcp). Parameter FR is termed as heat removal factor and is given by
(16)FR=(GcpUL)[1-exp⁡(-F′ULGcp)],
where F′ is termed as efficiency factor. It is given by(17)F′=(1+ULh)-1.The mean air temperature equation in terms of heat removal factorFR and efficiency factor F′ is(18)Tm=Ti+[Q(AULFR)]×(1-FRF′).The accuracy of the results of the performance analysis strongly depends on the use of appropriate heat transfer and friction factor correlations for the solar air heater ducts.For the asymmetrically heated high aspect ratio rectangular ducts of smooth duct solar air heater, Karwa et al. [8] used the following correlation of Ebadian and Dong [23, Equations (5.206) and (5.207)] for the apparent friction factor in the laminar regime, which takes account of the increased friction in the entrance region of the duct (19)fapp=24Re+(0.64+(38/Re))Dh(4L).The heat transfer correlation from Hollands and Shewen [24] for the thermally developing laminar flow for the smooth duct is(20)Nu=5.385+0.148Re(HL)forRe<2550.The friction factor correlation of Bhatti and Shah [25] for the transition to turbulent flow regime in rectangular cross-section smooth duct (0≤H/W≤1) is(21)f=(1.0875-0.1125HW)fo,
where(22)fo=0.0054+2.3×10-8Re1.5for2100≤Re≤3550,fo=1.28×10-3+0.1143Re-0.311for3550<Re≤107.They report an uncertainty of ±5% in the predicted friction factors from the above correlation.Considering the entrance region effect, the apparent friction factor in the turbulent flow regime is determined from the following relation for flat parallel plate duct [25]:(23)fapp=f+0.0175(DhL).The Nusselt number correlations for the transition and turbulent flow regimes in the rectangular solar air heater duct from Hollands and Shewen [24] are(24a)Nu=4.4×10-4Re1.2+9.37Re0.471(HL)for2550≤Re≤104(transitionflow)(24b)Nu=0.03Re0.74+0.788Re0.74(HL)for104<Re≤105(earlyturbulentflow).An uncertainty of an order of 5%-6% in the predicted Nusselt number can be expected [8]. As suggested by Karwa et al. [8], the laminar regime has been assumed up to Re=2800.The pressure loss and pumping power are calculated from(25)δp=[(4fappL)2ρDh](mWH)2P=(mρ)δp.The thermophysical properties of the air have been taken at the corresponding mean temperatureTm or Tmpg from the following relations of thermophysical properties, obtained by correlating data from NBS (U.S.) [26]:(26)cp=1006(Tm293)0.0155,k=0.0257(Tm293)0.86,μ=1.81×10-5(Tm293)0.735,ρ=1.204(293Tm),Pr=μcpk.Equations (1) to (26) constitute a nonlinear model for the solar air heater that has been used for the computation of the useful heat gain, thermal efficiency, and pumping power. The model has been solved by following an iterative process as depicted in Figure 3. For the heat collection estimate, the iteration was terminated when the successive values of the plate and mean air temperatures differed by less than 0.05 K. The iteration for the estimate of top loss has been continued till the heat loss estimates from the absorber plate to the glass cover and glass cover to the ambient; that is, Qtpg and Qtgo differed by less than 0.2%.Figure 3
Flow chart for iterative solution of mathematical model.


## 3. Experimental Setup

The experimental test facility, designed and fabricated as per ASHRAE Standard  for testing of solar collectors [27], consists of 300 mm wide parallel ducts with entrance, test, exit, and mixing sections, a blower, control valves, orifice plates and provision for temperature, and pressure drop measurements as shown in Figure 4. It works in an open loop mode. The ducts are made of good quality smooth faced plywood and wooden boards. Each duct is 2880 mm long consisting of 550 mm long insulated entry and exit sections and 1.62 m long test section. The height of both the ducts has been kept fixed at 38.4 mm. The combined width of ducts (with side walls) is 850 mm.Figure 4
Experimental setup.The test section of one of the parallel ducts carries 3.25 mm thick aluminium plate in 12 equal width pieces as absorber plate with twelve aluminium sections 0.9 mm thick installed as baffles. Each baffle consists of one row of holes as shown in Figure1(a). The other duct carries a three-piece smooth surfaced aluminium absorber plate. The sun-facing sides of both the absorber plates are smooth and blackened. Glass plates of 4 mm thickness have been used as cover over the absorber plates at a height of 60 mm. The top side of entry and exit lengths of each duct is covered with the plywood.A 100 mm long baffled mixing section is provided to get uniform temperature of the exit air in the measuring section just after the mixing section. The exit end of each duct is connected, through a rectangular to circular transition piece, to a 68 mm ID G.I. pipe with orifice plate assembly. The throat diameter of the orifice plate is 38 mm. The other end of the each pipe is connected through control valve to the suction of a 10 HP blower using flexible pipe and a Y-section (not shown in the figure).50 mm thick thermocole insulation has been provided on the back of the collector from test section inlet to outlet of twin duct, while the transition pieces and orifice plate assembly pipes (up to the orifice plates) are covered with foam blanket insulation. All joints are properly sealed with putty. The setup was installed horizontal (in north-south orientation) on the roof top at a height of 750 mm on an iron stand.Butt-welded 0.36 mm calibrated copper-constantan thermocouples have been used for various temperature measurements. For the plate temperature measurement, thermocouples have been fixed with M-seal in the sun-facing side of absorber plate in small diameter holes drilled about 2.5 mm deep at nine and fourteen axial locations on the smooth and baffled absorber plates, respectively, as shown in Figure4. Additional thermocouples have been affixed on the absorber plate of the baffled solar air heater to measure span wise variation of plate temperature. Three thermocouples are placed in temperature measuring section after the mixing section to measure the outlet air temperature, while a thermocouple placed midway in the entry section measures the inlet air temperature.Inclined U-tube manometers have been used for the measurement of pressure drop across the orifice plates. Pressure taps, located along the axial center line of the smooth lower wall of the both test sections, have been used to measure the static pressure drop across 1.62 m long test section using a null balance type micromanometer having a least count of 0.02 mm.Calibrated precision solarimeter and pyranometer have been used for the measurement of the intensity of the solar radiation on the collector plane. The wind velocity has been measured by an anemometer.The details of the half-perforated baffles employed in the study and other experimental conditions are given in Table1. The baffles have one row of holes (3/8′′ diameter) drilled in the lower half (near to the duct wall).Table 1
Baffles and test duct details and experimental conditions.
Baffles (half-perforated baffles):Baffle thickness,δ = 0.9 mmHeight,e = 19 mmPitch,p = 134.1 mmRelative baffle pitch,p/e = 7.06Open area ratio,β = 26%Arrangement: transverse to the flowDuct:Width,W = 298 mmHeight,H = 38.4 mmLength,L = 1620 mmHydraulic diameter,Dh= 68 mmBaffle to duct height ratio,e/H = 0.495Duct width to height ratio,W/H = 7.77Collector aperture area,Aa= 0.4×1.62 m2Experimental conditionsMass flow rate of air per unit area of the absorber plate,G≈ 0.02–0.073 kgs−1m−2Flow Reynolds number, Re≈ 3000–11000Solar insolation,I=585–710 Wm−2Wind velocity = 0.05–1.1 m s−1The open area ratioβ of the perforated baffles is defined as the ratio of the area of the holes to the baffle frontal area given by(27)β=n(π/4)D2be,
where n is the number of the holes drilled, D is the diameter of a hole, e is the height and b is the width of the baffle.Before starting the experiment, the setup and various components were checked for proper functioning. The glass covers were cleaned. Then, the blower was switched on, and the flow control valves were adjusted to give desired air flow rates through the ducts. All observations were made every 30 minutes starting from about 10 am till about 2 pm, that is, equally divided about the noon.


## 4. Data Reduction

The mass flow rate of air is determined from the measured pressure dropΔpo across the orifice plate(28)m=cdAo2ΔpopaRTo.Mass flow rate per unit area of the absorber plateGis calculated from
(29)G=mA,
where A=WL is the absorber plate area.The Reynolds number of the flowing air in the duct is calculated from(30)Re=G1Dhμ,
where G1=m/(WH) is mass velocity of air in the duct and Dh=4WH/[2(W+H)] is the hydraulic diameter of the duct.Useful heat gainQ is the heat transferred to the air from the heated absorber plate and is obtained from(31)Q=mcp(To-Ti).Thermal efficiencyη of the collector is ratio of useful heat gain to the incident solar radiation on the collector aperture area Aa(32)η=QAaI.The heat transfer coefficient has been calculated from(33)h=Q[A(Tp-Tm)],
where Tp is mean plate temperature calculated as the weighted average of temperature readings noted at various points along the axial length of the absorber plate; that is,(34)Tp=(1A)∑(TiAi).In (33), Tm is the mean air temperature taken as arithmetic mean of the measured inlet and outlet air temperature values(35)Tm=Ti+To2.From the known values of pressure dropΔpd across the test section and the mass flow rate, the pumping power is obtained from(36)P=(mρ)Δpd.
From the analysis of uncertainties in the measurements by various instruments [28], the uncertainties (odds of 20 : 1) in the calculated values of various parameters have been estimated as follows:flow rate per unit area of absorber plate,G=±1.6%,heat collection rate,Q=±3.8%,thermal efficiency,η=±4.9%,pumping power,P=±4.3%.


## 5. Results and Discussion

The experimentally determined thermal efficiency data for the smooth duct solar air heater are plotted in Figure5 against the flow rate per unit area of the absorber plate along with the predicted thermal efficiency from the mathematical model at the average values of the observed solar insolation, ambient temperature, and wind velocity during the experimentation. The absorber plate emissivity εp has been assumed to be 0.95, long wave emissivity of glass εg as 0.88, and transmittance-absorptance productτα as 0.8. The scatter in the experimental data is due to the variation in the ambient conditions. The theoretical analysis shows that the variation in the wind velocity has greater effect as compared to the variation in the ambient temperature and solar insolation in the experimental range of these parameters. At the lowest flow rate of the study, the experimental value of the thermal efficiency is lower due to a comparatively higher average wind velocity during experimentation at this flow rate, while the reverse is true at the highest flow rate of the study. Further, it is worth to note that, in general, the ambient temperature has been seen to rise with time (10 am to 2 pm) while the solar insolation increased up to the noon and then decreased. Thus, a transient condition exists, and the efficiency values in the morning and afternoon tend to lie below and above the mean values, respectively. Hence, looking to the effect of variation in the experimental conditions, the experimental and predicted values can be regarded to be in good agreement, and the presented model can be used to predict the performance of the solar air heater under a wide range of ambient (solar insolation, wind velocity, and ambient temperature) and air mass flow rate conditions.Figure 5
Thermal efficiency versus the flow rate per unit area of absorber plate for smooth duct air heater.For prediction of the performance of a roughened or baffled duct solar air heater, the Nusselt number and friction factor correlations of smooth duct air heater in the mathematical model are to be replaced by the appropriate correlations for the employed roughness or baffles.It can be seen in Figure5 that the thermal efficiency increases with increase in the flow rate, which is due to the increase in the heat transfer coefficient at the increased air velocity in the air heater duct.Figure6 shows the enhancement in the thermal efficiency due to the use of baffles on the air flow side of the absorber plate. The efficiency ratio in Figure 6 is the ratio of the thermal efficiencies of the baffled and smooth duct air heaters. The employment of the baffles enhances the thermal efficiency by about 28%–45%; higher gain is at the lowest air flow rate of the study. The thermal performance advantage of the baffled duct solar air heater can be attributed to the heat transfer enhancement (h/hs, where hs refers to the smooth duct) of about 180%–235% as depicted in Figure 7. The effect of the perforated baffles on the flow structure and resulting heat transfer enhancement has been discussed earlier.Figure 6
Efficiency ratio versus the flow rate per unit area of absorber plate.Figure 7
Heat transfer enhancement versus the flow rate per unit area of absorber plate.The increase in the heat transfer coefficient due to the baffles also reduces the mean absorber plate temperature of the baffled absorber plate by about 20°C–25°C as compared to the smooth duct air heater absorber plate; see Figure8. This leads to a reduction in the heat loss from the collector, which is a function of the excess of the absorber plate temperature over the ambient temperature. The increase in the heat collection rate due to the heat transfer enhancement and decrease in the heat loss from the collector due to the lower working temperature of the absorber plate enhance the thermal efficiency of the baffled air heater.Figure 8
Absorber plate temperature depression.The pumping power requirement has been found to be negligible (less than 0.5% of the heat collection rate). Thus, thermohydraulically, the baffled duct solar air heater is better than the smooth duct solar air heater.


## 6. Performance Prediction of Baffled Duct  Air Heater

For half-perforated baffles in an asymmetric heated rectangular duct, Karwa and Maheshwari [18] have presented the following correlations of Nusselt number and friction factor:
(37)Nuf=0.0893Re0.7608,=0.1673Re-0.0213,
with standard deviation of 1.34% and 3.34%, respectively, from the experimental data.Using the mathematical model presented above, performance study of baffled duct solar air heater has been carried out by replacing the Nusselt number and friction factor correlations for the smooth duct in the mathematical model by the above correlations for the baffled duct solar air heater. Table2 gives values of different parameters used in the study.Table 2
Values of different parameters for performance prediction of baffled duct solar air heater.
Collector width,W1 mCollector length,L2 mDuct height,H35 mmGap between absorber plate and glass cover50 mmCollector slope,β0° for horizontalNumber of glass covers1Transmittance-absorptance product,τα0.8 for single glass coverThickness of glass cover4 mmThermal conductivity of glass cover0.78 Wm−1 K−1Thermal conductivity of back insulation material (Thermocol)0.037 Wm−1 K−1Back insulation thickness50 mmLong wave emissivity0.88 for glass cover0.95 for absorber with flatblack paintRelative baffle height,e/H0.495Relative baffle pitch,p/e7.0Sky temperature,Ts=TaAmbient temperature,Ta285–315 KWind heat transfer coefficient,hw5 and 10 Wm−2 K−1Solar insolation,I500 and 800 Wm−2In Figure9, the plots of thermal efficiency and effective efficiency of the baffled duct solar air heater are presented against the temperature rise parameterΔT/Ifor fixed geometric and ambient parameters. Their values are also given in a tabular form. The effective thermal efficiency takes account of pumping power and is defined as [19](38)ηeff=(Q+P-P/C)IA.Figure 9
Thermal efficiency and effective efficiency as function of temperature rise parameter (W=1m, L=2m, H=0.035m, I=800W/m2, slope=0 deg; hw=5W/m2K, Ta=300K, and G=0.02–0.07 kg/sm2).In the above equation, factorC is a conversion factor for calculating equivalent thermal energy for the pumping power. It is a product of efficiency of fan, motor, transmission and that of thermoelectric conversion at the power plant. For a fan-motor efficiency of 0.6 and thermoelectric conversion efficiency referred to the consumer point as 0.33, the factorC works out to be 0.2. It is to note that pumping power P required to overcome friction is also converted into heat.It can be seen in Figure9 that the pumping power is not of a concern at low flow rates. At the highest flow rate of the study (G=0.07kg/sm2), the effective efficiency is about 5% lower than the thermal efficiency as also given in the table.The plot in Figure9 can be utilized for performance prediction of such air heater. The use of the plot is simple. For example, let for a given application the required air temperature rise is 12°C when solar insolation is 800 W/m2. Then, the temperature rise parameter ΔT/I works out to be 0.015. A vertical line on the plot in Figure 9 at ΔT/I=0.015 gives thermal efficiencyη of about 67.5%. Using the basic equation of thermal efficiency, the air mass flow rate per unit area of the absorber plate is estimated as
(39)G=(ηI)[cpΔT]=(0.675×800)(1005×12)=0.045kg/sm2.


## 7. Effect of Variation of Ambient Parameters on Thermal Efficiency

The performance plot in Figure9 has been presented for fixed values of solar insolation, wind velocity, and ambient temperature. These parameters, especially the solar insolation and ambient temperature, vary from morning to evening (9 AM to 4 PM) and also with the season of the year. The effect of their variation on the thermal efficiency of the baffled duct solar air heater is presented in Figures 10, 11, and 12Figure 10
Effect of ambient temperature (W=1 m, L=2 m,H=0.035 m, slope=0 deg; I=800 W/m2, hw=5 W/m2K).Figure 11
Effect of wind heat transfer coefficient (W=1 m,L=2 m, H=0.035 m, slope=0 deg; I=800 W/m2, Ta=300 K).Figure 12
Effect of solar insolation (W=1m, L=2m, H=0.035m, slope=0 deg; hw=5 W/m2K, Ta=300 K).From Figures10–12, it can be seen that effect of variation of the solar insolation from I=800W/m2sto 500W/m2 is not significant, while the increase in wind heat transfer coefficient from 5 W/m2K to 10 W/m2K reduces the thermal efficiency at the lowest flow rate by about 4%, which can be termed as significant. At the highest flow rate of the study (the lowest temperature rise parameter and extreme left end of these curves), the thermal efficiency is less affected by variation of these parameters. The thermal performance of the air heater improves by about 1.8% in the winter (Ta=285K) and reduces by about 2% in summer (Ta=315K) at the lowest flow rate. At low ambient temperature and solar insolation, the operating temperature of the collector reduces and thermal efficiency improves, while a high wind velocity increases the heat loss from the collector.The results of the present study can be utilized for the development of enhanced performance solar air heater with half-perforated baffles.


## 8. Conclusions

An experimental study on thermal performance of a solar air heater having half-perforated baffles on the air flow side of the absorber plate has been carried out for air mass flow rate of about 0.02–0.073 kg/s per m2 of the absorber plate area. A direct comparison of performance with the smooth duct solar air heater has been made, and a detailed mathematical model has been presented. The main findings of the present study are as follows.(1)
The predicted values of thermal efficiency from the mathematical model for the smooth duct solar air heater are in good agreement with the experimental data. Hence, the model can be used for performance prediction under wide range of operating and ambient conditions.(2)
The thermal efficiency of the baffled duct solar air heater is about 28%–45% higher than the smooth duct solar air heater; highest thermal performance advantage is at the lowest flow rate of the study.(3)
The heat transfer enhancement due to the baffles (of the order of 180%–235%) increases the heat collection rate and reduces the mean temperature of the baffled absorber plate by 20°C–25°C as compared to the smooth one.(4)
The pumping power requirement is only a small fraction of the heat collection rate in the range of the present study.(5)
Effect of variation of solar insolation on the thermal performance is negligible (0.4%–1.42%), while the variation in wind heat transfer coefficient affects the efficiency by 1.6%–4.3% and the ambient temperature by (±0.8%) to (±2.0%); the higher values in all cases refer to the lowest flow rate of the study.



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*Source: 634025-2011-10-19.xml*