Thermal Performance of Solar Air Heater Having Absorber Plate with V-DownDiscrete Rib Roughness for Space-Heating Applications

e paper presents results of thermal performance analysis of a solar air heater with v-down discrete rib roughness on the air �ow side of the absorber plate, which supplies heated air for space heating applications. e air heater operates in a closed loop mode with inlet air at a �xed temperature of 295K from the conditional space.e ambient temperature varied from 278K to 288K corresponding to the winter season ofWestern Rajasthan, India.e results of the analysis are presented in the form of performance plots, which can be utili�ed by a designer for calculating desired air �ow rate at different ambient temperature and solar insolation values.


Introduction
Flat plate solar air heaters have been employed for space heating, drying, and similar industrial applications requiring heated air at low to moderate temperatures.e thermal efficiency of a solar air heater (collector) is a function of many design and operating parameters.Convective heat transfer coefficient between the absorber plate and air �owing through the collector duct is one of the key parameters.
Arti�cial roughness on heat transferring surface of asymmetrically heated high aspect ratio rectangular ducts, modeled as solar air heater ducts, has been shown to signi�cantly enhance the heat transfer coefficient with minimum pressure loss penalty because the roughness creates turbulence near the heat transferring surface only [1][2][3][4][5][6][7].us such roughness can be used on the air �ow side of the absorber plate of the solar air heaters as shown in Figure 1(a) for the improvement of their thermal efficiency.
Figure 1(b) depicts the basic roughness geometries compiled by Karwa et al. [8], which includes different rib arrangements, such as transverse, angled, continuous, and discrete, in v-pattern for ribs of different shapes (circular, square, chamfered, wedge, etc.), and expanded metal wire mesh.Arti�cial roughness on a heat transferring surface creates local wall turbulence due to a complex �ow structure depending on the shape and arrangement of the ribs and hence the degree of the heat transfer enhancement in both the heat transfer coefficient and friction factor also varies with the roughness type.
Heat transfer enhancement in the case of the inclined or the v-pattern ribs has been reported to be higher than the transverse ribs [9].e enhancement in the case of the transverse ribs (at   ) occurs only due to the �ow, separated at the ribs, reattaching between the ribs while it has been attributed both to the reattachment effect and the secondary �ow of the air induced by the rib inclination in the case of inclined and v-pattern ribs [7,9] as depicted in Figure 2. e secondary �ow (movement of heated air in contact with the plate surface) is along the plate surface to the side wall in the case of the inclined ribs.is exposes the heated plate to a relatively lower temperature air of the axial or primary �ow over the ribs.In the case of v-down ribs, there are two contradictory effects: the secondary �ow is towards the central axis where it interacts with the axial �ow W W (iv) V-discrete rib roughness [7] Flow (vi) Chamfered ribs [4] (vii) Wedge shaped roughness [5] (v) Circular cross-section wire as ribs [1,2,6] φ l (iii) Circular cross-section wire in v-pattern [6] (ii) Expanded metal wire mesh [3]  (at  in Figure 2) creating additional turbulence leading to the increase in the heat transfer rate while the rise in temperature of the axial �ow air, just above the ribs in the central region due to the mixing of the secondary �ow, reduces the heat transfer rate.For the discrete ribs, the heated air moving as secondary �ow mixes with the primary air a�er only a short distance movement leading to a better mixing of the heated air near the plate with the colder primary air.In the case of crossed wire mesh, the �ow structure is quite complex.For example, the axial distance   / between the rib elements of the mesh of R. P. Saini and J. S. Saini [3] varies from 0 to 25. e primary �ow over the mesh portion with 7 <   /   causes enhancement due to the reattachment effect, while the �ow between 0 <   /  7 contributes poorly due to the vortex �ow.e secondary �ow mainly occurs along the rib elements where   / is greater than 7 and thus is likely to be less strong.e secondary �ow air, here also, mixes a�er a short distance movement with the primary �ow over the ribs at .Various studies report different degrees of enhancements in heat transfer and friction factor because of the difference in the �ow structure as discussed above.us the preference of any roughness type must be based on the objective of heat transfer enhancement with minimum pressure loss penalty and hence a thermo-hydraulic performance analysis is desired.Based on the criterion of equal pumping power, Karwa et al. [8] carried out a comparison of different roughness geometries depicted in Figure 1(b) to �nd out the preferred type of roughness for the absorber plate of a solar air heater.ey have recommended discrete rib roughness geometry of Karwa et al. [7] for applications such as space heating requiring heated air with temperature rise of the order of 15 ∘ C-25 ∘ C.
Karwa and Chauhan [10] carried out studies on thermal and effective efficiencies of solar air heaters, with open loop operation, having 60 ∘ v-down discrete rectangular crosssection repeated rib roughness on the air �ow side of the absorber plate using a mathematical model, which was validated against experimental data.e efficiency of the solar air heater is de�ned as where  is the useful heat gain,  is the incident solar radiation intensity on the collector plane,  is the area of solar air heater receiving solar radiation, Δ is the rise in the temperature of the air, and   is the air �ow rate per unit area of the absorber plate.e effective efficiency   , in their study, is based on the net gain aer taking account of the pumping power: where  is a conversion factor used for calculating equivalent thermal energy for obtaining the pumping power.It is a product of the efficiencies of the fan, electric motor, transmission, and thermoelectric conversion.ey concluded that the preferred relative roughness height is 0.07 for a solar air heater to be used for space heating applications, where the air �ow rate per unit area of the absorber plate is on the lower side (   kgs −1 m −2 ).

Objective
From the literature review presented above, it can be inferred that roughened duct solar air heaters can provide enhanced thermal and thermo-hydraulic performance.For low mass �ow rates applicable to space heating applications, the previous studies have established that the 60 ∘ v-down discrete rib roughness of Karwa et al. [7] is the preferred one.However, results of studies on the performance of such roughened solar air heaters operating in a closed loop for space heating applications are not available in the open literature.Hence, the present study has been planned to carry out performance studies on solar air heaters with 60 ∘ v-down discrete rib roughness of Karwa et al. [7] on the air �ow side of absorber plate for closed loop operation, where the inlet temperature of the air coming from the conditional space is constant.e analysis in the present study will be carried out by suitably modifying the mathematical model of Karwa and Chauhan [10].

Mathematical Model for Thermal
Performance Prediction e model used by Karwa and Chauhan [10] is based on the nonlinear mathematical model presented for a smooth duct solar air heater by Karwa et al. [11], which was suitably modi�ed by them for the study of roughened solar air heaters in their work.is 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 roughened and smooth duct air heaters.is model has also been modi�ed by them to estimate the collector back loss from the iterative solution of the heat balance equation for the back surface for greater accuracy.e edge loss has been calculated from the equation suggested by Klein [12].Figure 3(a) depicts the schematic diagram of a solar air heater and its longitudinal section along with plan of the roughened absorber plate having 60 ∘ v-down discrete rib roughness of Karwa et al. [7].
e heat balance on a solar air heater gives the distribution of incident solar radiation  into useful heat gain  and various heat losses as depicted in Figure 3(b).e useful heat gain or heat collection rate of the collector is where  is the area of the absorber plate, () is the transmittance-absorptance product of the glass coverabsorber plate combination.e overall heat loss   from the air heater is a sum of the losses from top   , back   , and edge   of the collector.e overall loss coefficient   is de�ned as where   is mean absorber plate temperature and   is ambient temperature.e collected heat is transferred to the air to be heated.us, e heat transfer coefficient ℎ between the air and absorber plate is determined from appropriate heat transfer coefficient correlation.e useful heat gain in terms of the heat transfer coefficient ℎ is where   is the mean temperature of air in the air heater duct.
3.1.Top Loss.e top loss   from the collector has been calculated from the iterative solution of basic heat transfer equations as detailed below.
Heat transfer from the absorber plate at mean temperature   to the inner surface of the glass cover at temperature   takes place by radiation and convection.Hence, e heat transfer through the glass cover of thickness   by conduction is where   is the thermal conductivity of the glass and   is temperature of the outer surface of the glass cover.
From the outer surface of the glass cover, the heat is rejected by radiation to the sky at temperature   and by convection to the ambient air.Hence, where ℎ  is the wind heat transfer coefficient.
In the equilibrium,   =   =   =   .e sky temperature   , in (7c), 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.One such widely used formula for clear sky is due to Swinbank [13], which is   = 0.0552  1.5   .
For the estimate of the convective heat transfer coefficient between the absorber plate and glass cover ℎ  the threeregion correlation of Buchberg et al. [14] has been used: where   is the gap between the absorber plate and glass cover.

Back and Edge
Losses.e back loss from the collector, refer Figure 3(b), has been calculated from the following equation: where  is insulation thickness and   is the thermal conductivity of the insulating material.Heat transfer by radiation from the heated absorber plate to the duct bottom surface is e heated bottom surface at temperature   transfers heat to the surroundings through the back insulation and to the air �owing through the duct at mean temperature   , that is, e absorber plate inner surface and duct bottom surface long wave emissivity values   and   in (11b) have been assumed to be 0.9.e heat balance for the back surface gives   =   .e temperature of the duct bottom surface   has been estimated from the iterative solution of this heat balance equation.
For the edge loss estimate, the following empirical equation suggested by Klein [12] has been used: where   is the area of the edge of the air heater transferring heat to the surroundings.e outlet air temperature has been estimated from e mean plate temperature equation in terms of heat removal factor   and efficiency factor  ′ is e parameter   in the above equation is given by the following relation: where  ′ in the above equation is de�ned as e outlet temperature of air in terms of   is e mean air temperature equation in terms of   and  ′ is Equations ( 14) and ( 17) have been used for the crosscheck of the values of temperatures   and   calculated from ( 6) and ( 13), respectively.
Knowing that 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, the model has taken extra care and efforts to select them.
For the asymmetrically heated high aspect ratio rectangular ducts of smooth duct solar air heater, Karwa et al. [11] used the following correlation of Chen in [15] for the apparent friction factor in the laminar regime: e last term in the equation takes account of the increase in the friction factor in the entrance region of the duct.e following heat transfer correlation from Hollands and Shewen [16] for the thermally developing laminar �ow for the smooth duct has been used: e friction factor correlation suggested by Bhatti and Shah [17] for the transition to turbulent �ow regime in rectangular cross-section smooth duct (0 ≤  ≤ 1 is where   = 0.0054 + 2.3 × 10 −8 Re 1.5 , for 2100 ≤ Re ≤ 3550,   = 1.28 × 10 −3 + 0.1143Re −0.311 , for 3550 < Re ≤ 10 7 . ( e reported uncertainty is ±5% in the predicted friction factor from the above correlation.
Considering the entrance region effect, the apparent friction factor has been determined from the following relation for �at parallel plate duct in the turbulent �ow regime [17]: e Nusselt number correlations used for the transition and turbulent �ow regimes from Hollands and �hewen [16] are: Nu = 3Re 4  88Re 4     for  4 < Re ≤  5 early turbulent �ow regime  (24b) e uncertainty of an order of 5-6% in the predicted Nusselt number has been expected [11].As suggested by Karwa et al. [11], the laminar regime has been assumed in the model up to Re = 28.e inconsistency of the predicted Nusselt number and friction factor values from the correlations presented above is about 5% at the laminartransition interface [11].
e friction factor and heat transfer correlations for the 60 ∘ v-down discrete rectangular cross-section repeated rib roughness used for the roughened duct solar air heater are [7]  =    45 , for 5 ≤   ≤ 5, e above set of (3) to (30) constitute a non-linear model for the solar air heater that has been used for the performance study.e model has been solved by following an iterative process presented in Figure 4.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, while 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,  tpg and  tgo from (7a) and (7c), respectively, differed by less than 0.2%.e mathematical model presented by Karwa and Chauhan [10] was validated by Karwa et al. [11] against the data from the experimental study of a smooth duct solar air heater published in an earlier work of Karwa et al. [21] with reported uncertainties of ±4.65% in Nusselt number and ±4.56% in friction factor.e standard deviations of the predicted values of thermal efficiency and pumping power from the experimental values of these parameters from Karwa et al. [21] have been reported by Karwa et al. [11] to be ±4.9% and ±6.2%, respectively.e uncertainties in the predicted values of various parameters for the roughened duct solar collector with 60 ∘ vdown discrete rib roughness of Karwa et al. [7] in the present work have been estimated to be ±6.4% in Nusselt number, ±5.9% in friction factor, ±7.3% in thermal efficiency and ±7.2% in pumping power.

Range and Values of Various Parameters
e range and values of the various parameters have been decided from the following considerations.
(1) e width  of air heater is usually kept as 1 m while the length  is 1-2 m, because of the constraints of available sizes of plywood and glass sheets, ease of installation and handling, especially for individual solar air heaters sloped to face south.(2) A low duct depth is favoured for high thermal efficiency of air heater.At �ow rates  ≤ 45 kgs − m −2 , Karwa and Chauhan [10] recommended a duct depth of 10 mm.
(3) Low cost solar air heaters employ an absorber plate with black paint, which gives short wave emissivity of 0.95.
(4) For maximum collection of solar energy in the winter, the collector slope  must be about 15 ∘ higher than latitude of the place.us, for Western Rajasthan (latitude ≈ 27 ∘ ) the optimum collector slope is about 45 ∘ .
(5) Since the solar air heater, under discussion, is meant for space heating, the inlet temperature of the air to the collector has been taken as 295 K for winter operation.
(7) e wind heat transfer coefficient ℎ  is a strong function of wind velocity.In Jodhpur, no wind to very mild wind condition exists in winter.e wind blows mainly from north to south.Since the collector is sloped to face south, any small variation in wind velocity will not affect the wind heat transfer coefficient signi�cantly.Hence, the present analysis has been carried out for a �xed value of 5 Wm −2 K −1 for the wind heat transfer coefficient.
(8) Solar radiation in Jodhpur, Rajasthan (India) varies from 500 Wm −2 at 9 am to around 1000 Wm −2 at the noon during a clear day in the winter on a south facing surface at 45 ∘ slope.Hence, in the present analysis, the solar insolation, , values have been considered to vary from 500 to 1000 Wm −2 .
(9) For space heating applications, a medium to high temperature rise of air is desired depending on the ambient temperature.Further, Karwa and Chauhan [10] have shown that at �ow rates less than 0.045 kgs −1 m −2 , roughened collector is thermohydraulically better than smooth duct air heater.Since the ambient temperature varies in the range of 5-15 ∘ C in winter in Jodhpur, a mass �ow rate of 0.01 to 0.045 kgs −1 m −2 per unit area of the absorber plate has been used in the analysis.(10) For space heating applications where �ow rates are not high and pumping power is not of much concern, a solar air heater with relative roughness height of 0.07 has been used as suggested by Karwa et al. [8] and Karwa and Chauhan [10].(11) For the air �ow rate per unit area of the absorber plate, the Reynolds number in the present study ranges from about 2000 to 9000.
e values of other collector parameters used in the analysis are listed in Table 1.
It is to note that the collector length may vary from 1 to 4 m.However, Karwa and Chauhan [10] have shown that, if the ratio of collector length to height of the duct ( is Roughened Smooth F 5: Enhancement in thermal performance due to arti�cial roughness (  2 m,   1 mm,  ℎ  .7,    .95,   5 ∘ , kept constant at 200, the variation in heat collection rate and hence the thermal efficiency of the collector for a given �ow rate does not change signi�cantly.us, the results of analysis presented here can be utilized for higher length collectors if  is kept constant.

Results and Discussion
e comparison of the thermal efficiencies of the roughened and smooth duct solar air heaters has been presented in Figure 5.It can be seen that the arti�cial roughness on the absorber plate signi�cantly improves the performance of the air heater, which is attributed to the heat transfer coefficient enhancement due to the arti�cial roughness on the air �ow side of the absorber plate.e enhancement in the thermal efficiency is 6-26%; the highest advantage can be seen at the lowest �ow rate of 0.01 kgs −1 m −2 of the study.ermal performance analysis of the roughened duct solar air heater has been carried out, using the mathematical model presented above, at three different ambient temperatures (278 K, 283 K, and 288 K). e air heater operates in closed loop mode with inlet air at a constant temperature of 295 K from the conditioned space.e results are presented in Figures 6-8 as performance plots, wherein the thermal efficiency values have been plotted against the temperature parameter [(  −    for �xed values of collector length   2 m, collector width   1 m, collector duct depth   1 mm, absorber plate emissivity    .95, collector slope   5 ∘ and wind heat transfer coefficient ℎ   5 Wm −2 K −1 , while air �ow rate ranges from minimum of 0.01 to the maximum of 0.045 kgs −1 per m 2 of the absorber plate.

Variation of ermal Efficiency with Flow Rate.
It is worth noting that the �ow rate is basically decided from the rise of the temperature of the air desired for a particular application.In the case of space heating applications, a constant temperature rise of the air may be desired.
Looking to the above mentioned basic requirement of constant temperature rise of the air for the space heating applications, lines of constant temperature rise (  −   ) = 10 ∘ C, 15 ∘ C, 20 ∘ C, and 25 ∘ C have also been plotted in Figures 6-8.From the study of constant temperature rise lines, it can be seen that, as the solar insolation increases, parameter (  −   )/ decreases and the air �ow rate must increase, and vice versa.us, from the morning (around 9 am) to noon, the �ow rate must increase with the increase in solar insolation and, then, must decrease from its maximum value in the noon again to the lowest value at around 4:30 pm.
From the constant temperature lines in the performance plots, the required �ow rate for a given temperature parameter value can be estimated from the plots.A correct value of the mass �ow rate per unit area of the absorber plate can be determined as explained below.
Let   = 283 K and solar insolation  is 800 Wm −2 .e desired temperature rise of the air (  −   ) is 15 K. en, for   = 295 K, (  −  )/ equals 0.015.A vertical line, as shown in Figure 7, cuts the (  −  ) = 5 K line at thermal efficiency  of 59.2%.From which, the mass �ow rate per unit area of plate  is calculated as: (31)

Effect of Ambient Temperature on ermal Efficiency.
Comparison of the performance plots in Figures 6-8 shows that the thermal efficiency increases with the rise in the ambient temperature.e analysis shows that, with change in the ambient temperature from 278 K to 288 K, the efficiency increases by 7.5% when solar radiation intensity is 500 Wm −2 , while the increase in the efficiency is 17.8% when  =  Wm −2 .is can be attributed to the fact that with the rise in the ambient temperature the heat loss from the collector reduces because of a lower temperature excess (plate temperature-ambient temperature).

ermo-Hydraulic
Performance.e requirement of the pumping power as fraction of the heat collection rate at the highest and the lowest solar insolation values is shown in Figure 9 as function of the mass �ow rate of the air through the collector duct per unit area of the absorber plate.At the highest �ow rate of  = .5kgs − m −2 and the lowest solar insolation  of 500 Wm −2 in the study, the pumping power is about 5.5% of the heat collection rate but this is not of much concern because at the low values of the solar insolation the �ow rate is also kept low to achieve a reasonable rise of the temperature of the air.It reduces to about 2.4% when  =  Wm −2 at the same �ow rate because of the greater heat collection rate.With the decrease in the �ow rate , the required pumping power decreases drastically.
For example, at  = .kgs − m −2 and I = 500 Wm −2 , the pumping power is less than 0.1% of the heat collection rate and is only 0.045% of the heat collection rate when solar insolation is 1000 Wm −2 .us, in the case of solar air heater  for space heating applications, the pumping power is not of much concern, that is, the thermo-hydraulic performance de�ned by ( 2) is not signi�cantly different from the thermal efficiency e�cept at the �ow rate   . kgs − m −2 .Hence, the plots of the effective efficiency   have not been drawn in the presented performance plots.

Conclusions
ermal performance analysis of a solar air heater with vdown discrete rib roughness has been carried out using a mathematical model.e collector, which supplies heated air for space heating application, is installed at a slope of 45 ∘ facing south and operates in a closed loop mode with inlet air at a ��ed temperature of 2�5 K from the conditional space in winter season of Western Rajasthan, India.e ambient temperature has been varied from 278 K to 288 K. e important observations of the study are as follows.
(1) e thermal efficiency of the roughened duct air heater is 6-26% higher than that of a smooth duct air heater� the highest advantage is at the lowest �ow rate of 0.01 kgs − m −2 of the study.(2) e mass �ow rate of air per unit area of absorber plate needs to be varied according to the variation in the solar insolation during the day for constant temperature rise of air through the collector and greater overall heat collection.(3) With the increase in the ambient temperature from 278 K to 288 K, the thermal efficiency increases by 7.5% to 17.8%, increasing with solar insolation.
(4) e pumping power requirement is not of concern at low �ow rates.At the highest �ow rate of   0.045 kgs −1 m −2 and the highest value of the solar insolation   1000 Wm −2 , it is the maximum and is of the order of 2.4% of the heat collection rate.
e results of analysis are presented in the form of performance plots with constant temperature rise lines of 10 ∘ C, 15 ∘ C, 20 ∘ C, and 25 ∘ C, which can be utilized by the designer for calculating desired air �ow rate under di�erent operating conditions.

𝛼𝛼:
Angle of attack, degree : Collector slope, degree   : Gap between the absorber plate and glass cover, m Δ: Temperature rise of air, ∘ C : ermal efficiency of collector : Emissivity  g : Kinematic viscosity of air at temperature   , m 2 s : Transmittance-absorptance product : Chamfer angle, wedge angle, degree : Dynamic viscosity of air, Pa⋅s.

F 3 :
e = height of rib w/e = relative roughness width = 2 p/e = relative roughness pitch = 10 B/S = relative roughness length of discrete ribs = (a) Longitudinal section of the roughened duct air heater with plane view of absorber plate having 60 ∘ v-down discrete rib roughness; (b) heat balance.

T 1 :
Values of parameters.Parameter Value Absorber plate-glass cover transmittance absorptance product,  0.8 (�xed) for single glass cover Gap between the absorber plate and glass cover,   40 mm Insulation Foamed polystyrene or glass wool ermal conductivity of insulation,   0.037 Wm −1 K −1 Insulation thickness,  50 mm Long wave emissivity of glass cover,   0− T a )/I (Km 2 W −1 )

GF 9 :
(kgs −1 m −2 ) Pumping power as percentage of the heat collection rate.