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Energy 55 (2013) 939e955

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Energy

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Performance study of solar air heater having v-down discrete ribson absorber plate

Rajendra Karwa a,*, Girish Chitoshiya b

a JIET School of Engineering & Technology for Girls, Mogra, National Highway No. 65, New Pali Road, Jodhpur 342 002, IndiabDepartment of Mechanical Engineering, Faculty of Engineering & Architecture, Jai Narain Vyas University, Jodhpur 342 011, India

a r t i c l e i n f o

Article history:Received 8 December 2012Received in revised form11 March 2013Accepted 26 March 2013Available online 29 April 2013

Keywords:Smooth and roughened duct solar air heater(collector)V-down discrete rib roughnessThermal efficiencyEffective efficiency

* Corresponding author. Tel.: þ91 291 2670 422. .E-mail address: karwa_r@yahoo.com (R. Karwa).

0360-5442/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2013.03.068

a b s t r a c t

The paper presents results of an experimental study of thermo-hydraulic performance of a solar airheater with 60� v-down discrete rib roughness on the airflow side of the absorber plate along with thatfor a smooth duct air heater. The enhancement in the thermal efficiency due to the roughness on theabsorber plate is found to be 12.5e20% depending on the airflow rate; higher enhancement is at thelower flow rate. The experimental data have been generated and utilized to validate a mathematicalmodel, which can be utilized for design and prediction of performance of both smooth and roughened airheaters under different operating conditions. The results of a detailed thermo-hydraulic performancestudy of solar air heater with v-down discrete rib roughness using the mathematical model are alsopresented along with the effect of variation of various parameters on the performance.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The thermal efficiency of a smooth duct flat plate solar air heateris low as compared to a solar water heater because of a low value ofheat transfer coefficient between the absorber plate and the flow-ing air, which leads to a higher temperature of the absorber plateand greater heat loss from the collector. In last two decades, theinvestigators have proposed employment of artificial roughness onthe airflow side of the absorber plate to enhance the heat transfercoefficient and hence the thermal efficiency of the flat plate solar airheaters [1e11]. Figs. 1 and 2 depict the different roughness shapesand arrangements, respectively, used by various researchers.

A catalogue of the flow structure for different rib roughnesstypes is presented as Fig. 3, which is an extension of the earlierpresentation by Karwa et al. [12], to explain the mechanisminvolved in the heat transfer enhancement due to the artificialroughness. In the case of rectangular or circular cross-section ribsarranged transverse to the flow at relative roughness pitch p/e of 7and higher, the flow separates at the ribs and reattaches in theinter-rib space. The laminar sublayer is practically completelydestroyed at the point of reattachment providing the highest heattransfer coefficient in the region around the reattachment point.

All rights reserved.

From the reattachment point, the boundary layer redevelopsdownstream while a re-circulating flow with occasional sheddingof vortices is established behind the ribs resulting in a poor heattransfer rate in thewake of the ribs, which extends up to the start ofthe reattachment region.

For roughened surfaces with positively chamfered ribs at rela-tive roughness pitch p/e � 5, vigorous vortex shedding has beenreported compared to the square or negatively chamfered ribs [13].Unlike square or rectangular section ribs, reattachment effect hasbeen reported for 15� chamfered ribs even at a lower relativeroughness pitch of 5. Thus the re-circulating flow region is reduced.

The rib elements which are not integral with the surface or notaffixed with the help of a resin are termed as detached ribs. A partof the flow passes through the gap between the plate surface andribs and improvement in the heat transfer rate in the wake of theribs is achieved [14].

The heat transfer enhancement has been reported to be morewhen the rib elements are arranged in inclined or v-pattern insteadof transverse pattern [3,9,10,15], which has been attributed to thesecondary flow of the air induced by the rib inclination as depictedin Fig. 3. The secondary flow (movement of the heated air in contactwith the roughened surface)moves towards the sidewall in the caseof the inclined ribs, towards both of the side walls in the case of theribs in v-up pattern or towards the center in the case of the ribs in v-downpattern. This exposes theheatedplate to the axiallyflowing air(termed as primary air) over the ribs, which is at a relatively lower

(a)

(iii) Wedge shaped roughness [6].

(b)

(i) Circular cross-section wire as ribs [1-3].

Wedge angle

Roughened absorber plate

p

eRibs

Air outAir in

Glass coverSolar insolation, I

L H Rib geometry

(ii) Chamfered ribs [4, 5].

Chamfer angle

Fig. 1. (a) Roughened duct solar air heater. (b) Rib shapes.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955940

temperature. In the case of v-down ribs, there are two contradictoryeffects. The secondary flow, moving towards the central axis, movesupwards (over the ribs) at the central axis and interacts with theaxial flow (at x in the figure) creating additional turbulence leadingto the increase in the heat transfer rate. At the other hand, the heattransfer is reduced because of the rise in temperature of the axialflow just above the ribs in the central region due to themixing of thehigh temperature secondary flow. Karwa [15] has confirmed thishypothesis. They observed that the centerline temperature of theheated air was higher in the case of the v-down arrangement of theribs as compared to ribs in the v-up arrangement.

In the ducts with discrete ribs, the secondary flow mixes withthe primary air flowing between the ribs after only a short distancemovement leading to a better mixing of the secondary flow nearthe plate surface with the primary flow. This effect improves withthe increase in the discretization of the ribs, which also indicates anincreased turbulence due to the vigorous mixing of the secondaryand primary flows [9].

In the case of crossed wire mesh of Saini and Saini [8], thedimensionless axial distance sx/e between the rib elements of themesh varies from 0 to 25, refer Fig. 3. The flow structure is quitecomplex [12]. In the region 0 < sx/e � 7, the flow contributes poorlyto the heat transfer enhancement because of the vortex dominantflow while, in the region 7 < sx/e � 25, enhancement occurs due tothe reattachment effect and the secondary flow is also present inthis region.

The enhancement in the heat transfer due to the artificialroughness is also accompanied with an increased frictional resis-tance to the flow. Hence, any scheme of roughness which provideshigh heat transfer enhancement with minimum pressure losspenalty is preferred. The studies presented above have reporteddifferent degrees of enhancements in heat transfer and friction

factor because both these effects are strong function of the flowstructure, which in turn depends on the geometrical parameters ofthe roughness as well as the flow Reynolds number.

Using the heat transfer and friction factor correlations reducedto the optimal conditions as defined by the investigators for theroughness geometries studied by them [1e4,6,8,9], Karwa et al. [12]carried out a comparison of thermo-hydraulic performance ofdifferent basic rib roughness types. Using the criterion of equalpumping power for the thermo-hydraulic performance compari-son, they report that, at low flow Reynolds number correspondingto low tomedium air mass flow rates per unit area of absorber plateemployed for space heating applications, the v-down discrete ribroughness of Karwa et al. [9] with relative roughness height of 0.06is better in performance than all other roughness types.

From the literature survey of the studies on asymmetricallyheated roughened rectangular ducts presented here, it can beinferred that v-down discrete rib roughness of Karwa et al. [9] isworth consideration for the development of an enhanced perfor-mance solar air heater. Though Karwa and Chauhan [16], using amathematical model, have presented a detailed performanceanalysis of solar air heater with such roughness, they validatedtheir mathematical model against the available experimental re-sults for smooth duct solar air heater and assumed that the modelmust be valid for the solar air heater with discrete rib roughness.

A solar air heater operates under a wide range of the ambientand operating parameters (I, Ta, Vw and G). The geometric anddesign parameters (L, H, dpg, εp, b, etc.) are selected according to theapplication of the air heater. A mathematical model is required topredict the performance of the solar air heater under differentconditions of operation and for different designs because carryingout experiments covering all the combinations of these parametersover a range is not a cost effective and practical proposition.

(iii) Expanded metal wire mesh [8].

Flow

(ii) Circular cross-section wire inclined to flow [1, 2].

(i)Transverse ribs [7].

W

Flow

s

l

Flow

(iv) Circular cross-section wire in v-pattern [3].

W

Flow

(v) V-down discrete rib roughness [9].

Flow

B

S60o

α

α

Fig. 2. Rib arrangements.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 941

Looking to the above discussion, the objective of the presentwork has been outlined as follows.

(i) To generate experimental data of thermal efficiency for solarair heaters with smooth duct and with v-down discrete ribroughness on the absorber plate in order to validate themathematical models of these air heaters, which can be uti-lized for the prediction of the performance of such air heatersunder different combinations of the design, operating andambient parameters according to the application.

(ii) To determine the performance enhancement due to the use ofthe roughness by comparing its performance with the simul-taneously procured experimental data for the smooth ductsolar air heater and also to validate the mathematical modelfor the smooth duct solar air heater.

2. Mathematical model of solar air heater

The model presented here has been adapted from Karwa andChauhan [16], which calculates the useful heat gain from the iter-ative solution of basic heat transfer equations of top loss andequates the gain with the heat transfer from the absorber plate tothe air. The model also estimates the back loss from the iterativesolution of the heat balance equation for the back surface of the airheater. Empirical equation of Klein [17] has been used for thecalculation of edge loss, which is basically a minor mode of the heatloss. Discussion on the uncertainty in the estimate of some of theimportant parameters that affect the accuracy of the performanceprediction has also been presented.

2.1. Useful heat gain

The heat balance on a solar air heater gives the useful heat gainQ or heat collection rate, refer Fig. 4a, as

Q ¼ AIðsaÞeQL: (1)

Product AI(sa) is the incident solar radiation intensity I over thecollector area A, which has been absorbed at the blackened sun-facing surface of the absorber plate having absorptivity a afterpassing through the glass cover of transmissivity s, and QL is totalheat loss from the collector.

The collected heat is transferred to the air flowing through thecollector duct. Hence,

Q ¼ mcpðToeTiÞ ¼ GA cpðToeTiÞ (2)

where G is mass flow rate of air per unit area of the absorber plate.From the heat transfer consideration, the heat gain can be

expressed as

Q ¼ hA�TpeTfm

�(3)

where Tp is the mean temperature of the absorber plate and Tfm isthe mean temperature of air in the collector duct.

The heat is lost from the top (Qt), back (Qb), and edge (Qe) of thecollector as depicted in Fig. 4a. Thus the total heat loss QL from thecollector is a sum of these losses, which have been estimated asexplained below.

2.2. Top loss, Qt

Heat is transferred from the absorber plate at temperature Tp tothe inner surface of the glass cover at temperature Tgi by radiationand convection as depicted in Fig. 4a. Hence,

Qtpg ¼ A�hrpg þ hpg

��TpeTgi

�(4)

where hrpg ¼ sðT2p þ T2giÞ ðTp þ TgiÞ=ð1=εp þ 1=εg � 1Þ, refer the

thermal network in Fig. 4b.Heat flows by conduction from the inner to the outer surface of

the glass cover of thickness dg and thermal conductivity kg hence

Qtg ¼ kgA�TgieTgo

��dg (5)

where Tgo is temperature of the outer surface of the glass cover.

x

(ii) V-down continuous ribs

α

x

(iii) V-down discrete ribs

Primary flow Secondary

x Mixing of primary and secondary flows

α

W

x

(i) Inclined ribs

x

x

x

(iv) Crossed wire mesh

sx

x

(iv) Wedge shaped ribs (iii) Chamfered ribs

(ii) Detached ribs

Penetrating flow Ribs

(i) Circular cross-section ribs

Re-circulating flowFlow reattachment

(a)

(b)

Fig. 3. (a) Effect of rib shape on the flow. (b) Effect of rib orientation on the flow.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955942

From the outer surface of the glass cover at temperature Tgo, theheat is lost by radiation to the sky at temperature Tsky and byconvection to the ambient air hence

Qtgo ¼ Ahhr�TgoeTsky

�þ hw

�TgoeTa

�i(6)

where hr ¼ sεgðT2go þ T2skyÞðTgo þ TskyÞ and hw is termed as wind

heat transfer coefficient. In the equilibrium,

Qtpg ¼ Qtg ¼ Qtgo ¼ Qt: (7)

The top loss Qt from the collector has been determined from theiterative solution of basic heat transfer equations presented above.

The sky is considered as a blackbody at some fictitious tem-perature Tsky known as sky temperature at which it is exchangingheat by radiation. Since the sky temperature is a function of manyparameters, it is difficult to make a correct estimate of it. In-vestigators have estimated it using different correlations. Onewidely used equation due to Swinbank [18] for clear sky is

Tsky ¼ 0:0552T1:5a (8)

where temperatures Tsky and Ta are in Kelvin.

(a)

(b)

Fig. 4. (a) Heat balance. (b) Thermal network of top and back loss.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 943

Another approximate empirical relation is [19]

Tsky ¼ Tae6: (9)

The above relations give significantly different values of the skytemperature except for the summer conditions in Western Rajas-than, India. Nowak [20] comments that, in the case of large cityareas, the sky temperature may be about 10 �C higher than the onecalculated from Swinbank’s formula because of the atmosphericpollution. The sky temperature also changes with the change in theatmospheric humidity. Thus, there can be significant uncertainty inthe estimate of the sky temperature, which may affect the pre-dicted thermal performance from any mathematical model.

For the estimate of the convective heat transfer coefficient hpgbetween the absorber plate and glass cover, the following three-region correlation of Buchberg et al. [21] has been used:

Nu¼ 1þ1:446ð1e1708=Ra cosbÞþ for 1708�Ra cosb�5900(10a)

(the þ bracket goes to zero when negative)

Nu ¼ 0:229ðRa cos bÞ0:252 for 5900 < Ra cos b � 9:23� 104

(10b)

Nu ¼ 0:157ðRa cos bÞ0:285 for 9:23� 104 < Ra cos b � 106

(10c)

where Ra is the Rayleigh number and b is the inclination of thecollector from horizontal. The Rayleigh number for natural con-vection heat transfer between parallel plates (absorber plate andthe glass cover in the present case) is given by

Ra ¼hg�TpeTgi

�d3pg=

�Tmpgv

2mpg

�iPr (11)

where dpg is the gap between the absorber plate and glass cover,refer Fig. 4a.

2.3. Back loss

The heat loss from the back surface of the air heater, refer thethermal network in Fig. 4b, is calculated from the followingequation:

Qba ¼ AðTbeTaÞ=ðd=ki þ 1=hwÞ (12)

where d is the insulation thickness and ki is the thermal conduc-tivity of the insulating material.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955944

The bottom surface of the air heater duct receives heat from theheated absorber plate by radiation, thus

Qpb ¼ As�T4peT

4b

��1=εpi þ 1=εb � 1

��1 (13)

where εpi and εb are long wave emissivity values of the absorberplate inner surface and duct bottom surface, which have beenassumed to be 0.9 in the present model.

A part of the received heat is lost from the back, Eq. (12), andremaining is transferred by convection to the air flowing throughthe duct at mean temperature Tfm, i.e.

Qbf ¼ hA�TbeTfm

�: (14)

The heat balance for the back surface gives

Qpb ¼ Qba þ Qbf : (15)

The back loss has been estimated from the iterative solution ofthe above heat balance equation.

2.4. Edge loss

The edge loss has been estimated from the empirical equationsuggested by Klein [17], which is

Qe ¼ 0:5Ae�TpeTa

�(16)

where Ae is the area of the edge of the solar air heater rejecting heatto the surroundings. From Eq. (2), the outlet air temperature is

To ¼ Ti þ Q=�mcp

�: (17)

The thermal efficiency h of the solar air heater is defined as theratio of the useful heat gain Q to the incident solar radiation on thecollector plane, i.e.

h ¼ Q=ðIAÞ: (18)

2.5. Friction factor and heat transfer correlations

2.5.1. Smooth ductFor the asymmetrically heated high aspect ratio rectangular

ducts of smooth duct solar air heater, Karwa et al. [22] recommendthe following friction factor and heat transfer correlations for the

Plan view

Roughened absorber plate

p

e

w

Ribs

Flow

S

Air in

Fig. 5. Roughened

laminar regime due to Chen [23] and Hollands and Shewen [24],respectively,

f ¼ 24=Reþ ð0:64þ 38=ReÞDh=ð4LÞ (19)

Nu ¼ 5:385þ 0:148ReðH=LÞ for Re < 2550: (20)

The heat transfer and friction factor correlations from Refs. [24]and [25], respectively, for the transition to turbulent flow regime inrectangular cross-section smooth duct (0 � H/W � 1), are asfollows.

Nu ¼ 4:4� 10�4Re1:2 þ 9:37Re0:471ðH=LÞfor 2550 � Re � 104ðtransition flowÞ ð21Þ

and

Nu ¼ 0:03Re0:74 þ 0:788Re0:74ðH=LÞfor 104 < Re � 105ðearly turbulent flowÞ: ð22Þ

Uncertainty of an order of 5e6% can be expected in the pre-dicted values of the Nusselt number [22].

f ¼ ð1:0875e0:1125H=WÞfo (23)

where fo ¼ 0:0054þ 2:3� 10�8Re1:5 for 2100� Re� 3550, andfo ¼ 1:28� 10�3 þ 0:1143Re�0:311 for 3550 < Re� 107 with anuncertainty of �5% in the predicted friction factor values.

Considering the entrance region effect, the apparent frictionfactor for a flat parallel plate duct in the turbulent flow regime[25] is

fapp ¼ f þ 0:0175ðDh=LÞ: (24)

The laminar regime has been assumed up to Re ¼ 2800 in thepresent analysis as recommended by Karwa et al. [22]. The incon-sistency of the predicted values of the Nusselt number and frictionfactor from the correlations presented above is about 5% at thelaminaretransition interface.

2.5.2. Roughened ductFig. 5 shows the 60� v-down discrete rectangular cross-section

repeated rib roughness which has been considered for the rough-ened duct solar air heater in the present study. The friction factorand heat transfer correlations, respectively, for this roughnessare [9]

w/e = relative roughness width = 2.06 p/e = relative roughness pitch = 10.63B/S = relative roughness length

of discrete ribs = 6 = angle of attack = 60o

B

Glass cover

absorber plate.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 945

R ¼ 6:06�eþ

�0:045for 15 � eþ � 75 (25)

g ¼ 15:69�eþ

��0:2for 15 � eþ < 25 (26a)

and

g ¼ 4:1�eþ

�0:217for 25 � eþ � 75 (26b)

where R is termed as roughness function, eþ is roughness Reynoldsnumber and g is heat transfer function. These functions are definedas [26,27]

R ¼ ð2=f Þ0:5 þ 2:5lnð2e=DhÞ þ 3:75 (27)

eþ ¼ ðf =2Þ0:5Reðe=DhÞ (28)

g ¼ ½ðf =2StÞ � 1�ð2=f Þ0:5 þ R (29)

where St (¼Nu/RePr) is the Stanton number.

2.6. Pumping power

From the estimate of the friction factor, the pressure loss andpumping power are calculated from the following equations.

dp ¼ ½ð4fLÞ=ð2rDhÞ�ðm=WHÞ2 (30)

P ¼ ðm=rÞdp: (31)

2.7. Thermophysical properties

The thermophysical properties of the air have been taken at thecorresponding mean temperature from the following relations,which have been obtained by Karwa et al. [22] by correlating datafrom NBS (U.S.) given in Holman [28],

cp ¼ 1006ðTm=293Þ0:0155 (32a)

k ¼ 0:0257ðTm=293Þ0:86 (32b)

m ¼ 1:81� 10�5ðTm=293Þ0:735 (32c)

r ¼ 1:204ð293=TmÞ (32d)

Pr ¼ mcp=k: (32e)

Eqs. (1) to (32) constitute a non-linear mathematical model forthe solar air heater. It has been used for the computation of theuseful heat gain Q, thermal efficiency h, pressure loss dp, pumpingpowerPandeffectiveefficiencyhe (as definedbelow). Themodel hasbeen solved by following an iterative process presented in Fig. 6 [16].

The wind heat transfer coefficient hw at the outer surface of theglass cover in Eq. (6) is a function of the wind velocity. Uncertaintyin the estimate of this coefficient has been discussed below.

2.8. Wind heat transfer coefficient

Various correlations for the estimate of the wind heat transfercoefficient hw from the wind velocity data are available in theliterature. Some of them are presented and discussed below.

(i) McAdams [29] proposed the following correlation:

hw ¼ 5:6214þ 3:912Vw for Vw � 4:88 m=s (33a)

¼ 7:172ðVwÞ0:78 for Vw > 4:88 m=s: (33b)

This correlation has been widely used in modeling, simulation,and relevant calculations in spite of its shortcomings [30].

(ii) Watmuff et al. [31] expressed the opinion that the wind co-efficient, derived from McAdams correlation includes radia-tion effect. They presented the following relation to excluderadiation and free convection contribution:

hw ¼ 2:8þ 3:0Vw for 0 < Vw < 7 m=s: (34)

(iii) Kumar et al. [32], based on indoor laboratory measurement onbox-type solar cooker, proposed the following correlation forthe wind heat transfer coefficient.

hw ¼ 10:03þ 4:68Vw: (35)

(iv) Test et al. [33] and Akhtar and Mullick [34] observed that, inthe outdoor environment, the convection heat transfer coef-ficient is greater than the values reported from wind tunneltests and gave the following correlation for rectangular plateexposed to varying wind directions.

hw ¼ ð8:355� 0:86Þ þ ð2:56� 0:32ÞVw: (36)

(v) Kumar and Mullick [35] experimentally determined the windheat transfer coefficient at low wind velocities (Vw < 0.37 m/s)fromametalplate exposed to solar radiation. Their correlation is

hw ¼ 0:8046�Tp � Ta

�0:69: (37)

The predicted values of the wind heat transfer coefficient fromthedifferent correlations presented abovevary significantly. Palyvos[30] expressed the opinion that the obvious lack of generality of theexisting wind convection coefficient correlations presents a chal-lenge for future research. Field rather than laboratory measure-ments, aswell as some sort of standardization in the choice of heightabove the ground and/or distance from the façade wall or roof withsuitable amendment of the velocity value on the basis of surfaceorientation and wind direction relative to the surface are required.

As mentioned earlier also, the uncertainty in the estimate of thewind heat transfer coefficient will have an impact on the accuracyof predicted thermal performance of a solar air heater using anymathematical model.

2.9. Thermo-hydraulic performance evaluation

Cortes and Piacentini [36] used effective thermal efficiency hefor the thermo-hydraulic performance evaluation of a solar col-lector. The effective thermal efficiency is based on the net thermalenergy gain considering the pumping power required to overcomethe friction of the air heater duct. Since the power lost in over-coming frictional resistance is converted into heat, Karwa andChauhan [16] defined the effective efficiency as

he ¼ ½ðQ þ PÞ � P=C�=ðIAÞ (38)

where C is a conversion factor used to calculate the equivalentthermal energy for obtaining the pumping power at the consumer

Fig. 6. Flow chart for iterative solution of mathematical model [16].

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955946

point. It is a product of the efficiencies of the fan, electric motor,transmission and thermo-electric conversion at the power plant.Based on assumption of 60% efficiency of the bloweremotor com-bination and 33% efficiency of thermo-electric conversion processreferred to the consumer point, factor C has been taken as 0.2 in thepresent study. Since the operating cost of a collector depends on thepumping power spent, the effective efficiency based on the netenergy gain is a logical criterion for the thermo-hydraulic perfor-mance evaluation of the solar air heaters.

The mathematical model presented here has been validatedagainst the experimental data, which has been generated byexperimentation on both the roughened and smooth duct solar airheaters in outdoor conditions as presented in the following sec-tions. The experimental study is also aimed at studying the

enhancement in the thermal efficiency due to the employment ofthe artificial roughness on the airflow side of the absorber plate.

3. Experimental setup

The experimental test facility used in the present work has beendeveloped as per the guidelines of ASHRAE Standard 93-77 (1977)for testing of solar collectors [37] using an open-loop system.

The setup, shown in Fig. 7, consists of wooden ducts made ofgood quality plywood and wooden boards with a very smoothfinish on the airflow duct surfaces. The parallel airflow ducts are300mmwidewith suitable entrance, test, exit andmixing sections.Each duct is 2880 mm in length and 38.4 mm in average height(depth). Entry and exit sections are 550 mm long in line with the

550

50

Elevation

Insulation

Air duct Mixing sectionInsulation

Absorber plateGlass cover

All dimensions in mm.(Not to scale)

400

Plan

125

125

300

300

Thermocouple locations

Roughened absorber plate Foam insulation

Smooth plate

Control valves

Orifice plate

Transition pieces

Inclined U-tubemanometer2880

1620

1000280

Orifice plate

Airin

Toblower

Pressure tapping

(a)

(b)

Fig. 7. (a) Experimental setup. (b) Photograph of experimental setup.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 947

recommendation of the ASHRAE code while the test section is1.62 m in length. For the test section, the length to hydraulicdiameter ratio is 24.25. The combined width of ducts (along withthe side walls) is 850 mm.

The test section of one of the ducts carries the roughenedabsorber plate at the top while the parallel test section carries asmooth surfaced absorber plate. The sun-facing sides of theabsorber plates are painted black for high absorptivity of the solarradiation incident after passing through the 4 mm thick glasscovers placed at a height of 60 mm above the absorber plates.

The 100mm longmixing section, provided after the exit section,consists of baffles with holes to provide uniform temperature of theexit air in the temperature measuring section provided after themixing section.

The exit end of each wooden duct is connected, through arectangular to circular transition piece, to a 68 mm inner diameterG.I. pipe with orifice plate assembly, which consists of orifice platehaving 38 mm throat diameter. The ends of the pipes are con-nected to the suction of a 10 HP blower through control valves

using flexible pipes and a Y-section (not shown in the figure of thesetup).

All joints were properly sealed with window or NC putty toensure air tightness. Fifty mm thick thermocole insulation has beenprovided over the exit section and also on the back of the air heaterassembly from test section inlet to outlet of twin ducts while thetransition pieces and pipes up to the orifice plates have beeninsulated by covering with foam blanket insulation.

Calibrated copper-constantan thermocouples (0.36 mm wirediameter) have been used for measurement of various tempera-tures. Twenty four thermocouples at 12 axial locations, as shown inFig. 8a, have been fixed with M-seal in the sun-facing side ofabsorber plate in small diameter holes drilled about 2e3 mm deepwhile thermocouples at nine axial positions have been fixed to thesmooth absorber plate as shown in Fig. 8b. Five thermocouples,placed in the temperature measuring section after the mixingsection of the roughened duct (three thermocouples in the case ofthe smooth duct), measure the outlet air temperature from the testsection, while a thermocouple placed midway in the entry section

(a) Roughened absorber plate.

1620

15

190 200105

195 195105

190 195100

25

300

50

300

1620

(b) Smooth absorber plate.

15

100195 205 155 200 195 195

65

295

Fig. 8. Thermocouple locations.

Table 1Test setup and experimental conditions.

Roughness Width, w ¼ 6.58 mmHeight, e ¼ 3.2 mmPitch, p ¼ 34 mmRelative roughness pitch, p/e ¼ 10.63Angle of attack, a ¼ 60�

Relative roughness length of discrete ribs B/S ¼ 6Arrangement: V-down discrete

Duct Width, W ¼ 300 mmHeight, H ¼ 38.4 mmLength, L ¼ 1620 mmHydraulic diameter, Dh ¼ 68 mmRelative roughness height, e/Dh ¼ 0.047Duct width to height ratio, W/H ¼ 7.8Collector aperture area, Ap ¼ 0.4 � 1.62 m2

Experimentalconditions

Mass flow rate of air per unit area of the absorberplate, G z 0.018e0.074 kg/s m2

Flow Reynolds number, Re z 2750e11,150Solar insolation, I z 550e670 W/m2

Wind velocity, Vw z 0.035e0.9 m/s

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955948

of the each duct measures the inlet air temperature. The thermo-couple output is fed to a millivoltmeter.

Inclined U-tube manometers (inclination of about 1 in 5) withmethyl alcohol have been employed for the measurement of pres-sure drop across the orifice plates. Pressure taps (6mm in diameter),along the axial centerline of the smooth bottomsides of the both testsections, have been provided to measure the static pressure dropacross the test section using a null balance type micro-manometerhaving a least count of 0.02 mm of methyl alcohol.

Calibrated pyranometer has been used for the measurement ofthe intensity of the solar radiation on the collector plane. The windvelocity just above the collector plane has beenmeasured by awindspeed meter. The local ambient temperature has been assumed tobe equal to the air inlet temperature.

The setup was installed horizontal (in northesouth orientation)on a roof top and it worked in an open-loop mode.

Before start of the experiment, the glass covers were properlycleaned. All joints were checked against leakage. It was assured thatall the instruments were working properly. The blower was startedat around 9.30 a.m. after about 30 min exposure of the collector tothe solar radiation. Before start of the blower, the control valveswere closed and then were slowly opened after start of the blower.The desired flow rate was adjusted by observing the reading of theU-tube manometer. Readings were taken after around 30 minrunning of the blower to ensure a near steady state condition.Pressure drop measurements for the ducts have been taken underisothermal condition.

The geometrical parameters of the test section, roughness pa-rameters and the experimental conditions, viz. flow rate, windvelocity and solar insolation during the experimentation are givenin Table 1, while Fig. 5 shows the roughened absorber plate used inthe present study. The test duct geometry, roughness parametersand the Reynolds number range in the present study are basicallythe same as reported by Karwa et al. [9] for their indoor experi-mental heat transfer and friction factor studies.

Experimental measurements have been made for five days atfive different flow rates between 10 a.m. and 2 p.m. every 30 min.The recorded data include solar insolation, ambient temperature,air inlet and outlet temperatures, plate temperature, overhead skyand glass temperatures using infrared thermometer, wind velocity,and pressure drop across the test ducts and orifice plates.

4. Data reduction

Useful heat gain Q is the heat transferred to the air from theheated absorber plate and is obtained from the known values of airinlet and outlet temperatures Ti and To, respectively. Thus

Q ¼ mcpðTo � TiÞ (39)

where m is the mass flow rate of the air through the collector duct.

0

10

20

30

40

50

60

70

80

90

0 0.02 0.04 0.06 0.08

The

rmal

eff

icie

ncy

(%)

G (kg/sm2)

Δ ExperimentalPredicted

Fig. 9. Experimental and predicted thermal efficiency for solar air heater withroughened plate.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 949

The mass flow rate has been determined from the measuredpressure drop Dpo across the orifice plate:

m ¼ CdAo

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2DpopaRTo

s(40)

where Ao is the area of the orifice, Cd is the coefficient of dischargefor the orifice plate, R is gas constant and pa is the ambient pressure.Outlet air temperature To is in Kelvin.

The average heat transfer coefficient has been calculated from:

h ¼ Q

A�Tpm � Tfm

� (41)

where Tpm is mean plate temperature. It has been calculated fromplate temperature readings noted at n locations along the axiallength of the absorber plate:

Tpm ¼ 1L

Xn1

Tpi � Li: (42)

In Eq. (41), Tfm is the mean air temperature in the collector duct.It has been taken as simplemean of inlet and outlet temperatures ofthe air, i.e.

Tfm ¼ 12ðTi þ ToÞ: (43)

Knowing the average heat transfer coefficient, the Nusseltnumber has been calculated from:

Nu ¼ hDhk

(44)

where Dh ¼ 4WH=½2ðW þ HÞ� is the hydraulic diameter of the ductand k is the thermal conductivity of the air at the mean air tem-perature Tfm.

Mass flow rate per unit area of the absorber plate G is calculatedfrom

G ¼ m=A (45)

where A ¼WL is the area of the absorber plate.The Reynolds number of the flow of air in the duct is calculated

from:

Re ¼ G1Dhm

(46)

where G1 ¼ m/(WH) is mass velocity of the air in the duct.Thermal efficiency h of the solar air heater is the ratio of useful

heat gain Q to the incident solar radiation on the collector aperture(area Ap):

h ¼ QApI

: (47)

From the known values of pressure drop Dpd across the testsection and the mass flow rate m, the friction factor f and pumpingpower P have been calculated from:

f ¼ 2DpdDh

4LG21

(48)

and

P ¼ mDpdr

: (49)

From the analysis of uncertainties in the measurements byvarious instruments [38], the uncertainties (odds of 20:1) in thecalculated values of various parameters have been estimated as[39]

Flow rate per unit area of absorber plate, G ¼ �1.6%Heat collection rate, Q ¼ �3.8%Thermal efficiency, h ¼ �4.9%Pumping power, P ¼ �4.3%

5. Results and discussion

Experimental measurements for both roughened and smoothduct solar air heaters have been taken simultaneously at differentflow rates as mentioned earlier. For the prediction of the solar airheater performance, the mathematical model for the smooth aswell as roughened duct solar air heater has been used with inputdata referring to the experimental conditions. For the performanceprediction from the model, the iteration was terminated when thesuccessive values of the plate and mean air temperatures differedby less than 0.05 K. The iteration for the estimate of top loss hasbeen continued till the heat loss estimates from the absorber plateto the glass cover and glass cover to the ambient, i.e., Qtpg and Qtgo,respectively, differed by less than 0.2%.

5.1. Thermal efficiency results and validation of the mathematicalmodel

The thermal efficiency values predicted by the mathematicalmodel have been plotted along with the experimental results forthe roughened duct and smooth duct solar air heater in Figs. 9 and10, respectively. The flow and geometrical parameters, and ambienttemperature, wind velocity and solar insolation values for theperformance prediction from the mathematical model refer to theactual experimental conditions, where the ambient temperature,wind velocity and solar insolation values are the average valuesrecorded during the experimentation at different flow rates underconsideration.

The scattering seen in the experimental data can be attributed tothe variation in the ambient temperature, solar insolation, wind

0

10

20

30

40

50

60

70

80

90

0 0.02 0.04 0.06 0.08

The

rmal

eff

icie

ncy

(%)

G (kg/sm2)

Δ ExperimentalPredicted

Fig. 10. Experimental and predicted thermal efficiency for smooth duct solar airheater.

200

250

300

350

1 2 3 4 5

Tsk

y (K

)

Day

Δ Ta

Tsky, Eq. (8)Tsky (overhead)

Fig. 11. Variation of the ambient (Ta), predicted sky and measured overhead sky (Tsky)temperatures on Day 1e5.

Table 2Estimate of the wind heat transfer coefficient hw (W/m2 K).

Vw (m/s) Eq. (33) Eq. (34) Eq. (35) Eq. (36) Eq. (37) Rangea

0 5.7 2.8 10.03 7.5e9.2 hw ¼ 6 W/m2 Kat Vw ¼ 0 m/s;hw ¼ 8 W/m2 Kat Vw ¼ 0.1 m/s

5.7e10.00.5 7.6 4.3 12.4 8.6e10.7 7.6e12.41.0 9.5 5.8 14.7 9.7e12.1 9.5e14.71.5 11.5 7.3 17.0 10.9e13.5 10.9e17.02.0 13.5 8.8 19.4 12.0e15.0 12.0e19.4

a Neglecting the values estimated from Eq. (34).

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955950

speed and angle of incidence of the solar radiation. The standardand average deviations of the predicted and experimental data areabout �11% and 8%, respectively, with major deviations at thelowest and highest flow rates; with excellent matching at middleflow rates. The likely reasons for the deviations at these flow ratesare being explained below.

There is uncertainty in the estimates of the sky temperature andwind heat transfer coefficient values used in the mathematicalmodel.

The sky temperature for the prediction of thermal performancehas been estimated from the Swinbank’s relation corresponding tothe prevailing ambient temperature, which has been found to varybetween 310 and 313.4 K during the days of the experiment. Bypointing the IR thermometer straight up at the sky (zenith), assuggested in Ref. [40], the sky temperature has been measured onall these days at every 30 min interval. However, the measurementof the sky temperature at various angles from the zenith has notbeen undertaken. The measurement of temperature straight up thesky has shown that the averaged sky temperature between10.30 a.m. and 1.30 p.m. varied significantly from Day 1 to Day 5 ofthe study. The recorded average sky temperatures on these dayswere 266 K, 274 K, 275 K, 281 K, and 285.5 K, respectively, while therecorded ambient temperature and the corresponding sky tem-perature (in brackets) calculated from Swinbank’s correlation are310.1 K (301.4 K), 313.4 K (306.3 K), 313.4 K (306.2 K), 311.6 K(303.6 K) and 310 K (301.3 K), respectively. These data have beenplotted in Fig. 11. It can be seen that the predicted value of the skytemperature varies only in a narrow range while the measuredoverhead sky temperature varied significantly (from 266 K to285.5 K). The Swinbank’s relation considers the sky temperature asa function of the ambient temperature and is applicable only for theclear sky condition. The significant variation in the recorded skytemperature may be attributed to the variation in the climaticconditions during the days of the experimentation. This affects thethermal performance of the collector.

A decrease in the sky temperature adversely affects the thermalefficiency of a collector because of the increase in the radiation heatloss from the glass cover surface to the sky and vice versa. Analysis,using the mathematical model of the present study, showed that a5 K change in the sky temperature estimate affects the thermalefficiency by 1.9%. It is seen in the plots of thermal efficiency for

both roughened and smooth duct collectors that the predictedthermal efficiency at the lowest flow rate (Day 1) was higher whenthe recorded overhead sky temperature was 266 K against theestimated value of 301.4 K, and similarly at the higher flow rate end(Days 4 and 5), the predicted efficiency was about 13% lower whenthe recorded overhead sky temperatures were higher by about 15e19 K than Day 1. Thus the uncertainty in the sky temperature es-timate may cause the predicted thermal efficiency value to deviateby about þ5% at the lowest and �5% at the highest flow rates.

Another possible major reason for the deviation in the predictedand experimental values of the thermal efficiencies is the uncer-tainty in the estimate of the wind heat transfer coefficient at theobserved wind speeds. The variation in the estimate of the windheat transfer coefficient from Eqs. (33)e(37) can be seen to besignificant as given in Table 2. A best possible estimate of the windheat transfer coefficient from these relations has been assumed asan average of the values given in column 7 of the table; keeping thefact in themind that the estimated valuemay have any valuewithinthe variation limit given in the column 7 of the table. A high windvelocity leads to a greater heat loss from the collector. This effect ismore pronounced at the lower flow rates because of the higheroperating temperature of the collector. The analysis shows that avariation of 1.0 W m�2 K�1 in the wind heat transfer coefficientaffects the thermal efficiency by 1.8% at the lowest mass flow rateand 0.35% at the highest mass flow rate of the present study.

Since the predicted heat transfer coefficients, from the correla-tions given in the mathematical model, have the uncertainty of theorder of 5%, the analysis has also been carried out to see the effect ofthis uncertainty. The result of the analysis at the experimentalconditions shows that a 5% change in the heat transfer coefficient

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 951

between the absorber plate and air flowing through the duct willaffect the predicted thermal efficiency by 2% at the lowest flow rateof the study and by 1.1% at the highest flow rate.

From the discussion of the effect of the uncertainties in the es-timate of various parameters on the predicted thermal efficiencyusing the mathematical model, it can be concluded that themathematical model presented, for both the smooth and rough-ened duct solar air heaters, can be utilized for prediction of the airheater performance. The accuracy of the prediction will, of course,depend on the accuracy of the estimate of sky temperature, windheat transfer coefficient and other parameters affecting the thermalperformance.

5.2. Variation of the thermal efficiency with the flow rate

The thermal efficiency of both the roughened and smooth ductsolar air heaters increases with the increase in the flow rate of theair per unit area of the absorber plate G as seen in Figs. 9 and 10.This can be attributed to the increased heat transfer coefficient

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06 0.08 0.1

Tpm

-T

a (K

)

G (kg/sm2)

0

10

20

30

40

50

60

70

0 0.02 0.04 0.06 0.08

Tpm

-T

a (K

)

G (kg/sm2)

(a) Roughened collector.

(b) Smooth duct collector.

Fig. 12. Plate temperature excess versus the mass flow rate per unit area of plate.

between the air flowing through the duct and the absorber platewith the increase in the Reynolds number. An increase in the heattransfer coefficient increases the heat collection rate and also re-duces the plate temperature, which in turn reduces the heat lossfrom the collector. The effect of the enhancement in the heattransfer coefficient on the absorber plate temperature can beobserved from Fig. 12a and b, where the plate temperature excess(mean temperature of the plate Tpm over the ambient temperatureTa) has been plotted against the flow rate G for the roughened andsmooth duct solar air heaters, respectively. The plate temperatureexcess for the roughened absorber plate is significantly lower(18.5e40.8 K) than the smooth duct (33e53.2 K), which clearlyindicates a low operating temperature and hence increased ther-mal efficiency due to the reduced heat loss from the roughenedduct solar air heater compared to the smooth duct air heater.

The enhancement in the thermal efficiency due to theemployment of the discrete rib roughness on the absorber plate hasbeen depicted in Fig. 13. At the present experimental conditions,the enhancement achieved in the thermal efficiency is 12.5e20%depending on the flow rate; the greatest enhancement is at thelowest flow rate of the study. The enhancement in the efficiencycan be termed as significant. The enhancement in the thermal ef-ficiency is attributed to the enhancement in the heat transfer co-efficient due to the employment of the artificial roughness. Fromtheir experiments for heat transfer, Karwa et al. [9] reported heattransfer enhancement of 56e121% over the smooth duct under thesame geometric and flow conditions as in the present study.

The friction factor results for both the solar air heater ducts havealso been found to be in reasonable agreement (5.7% average de-viation) with the predicted data from the roughness functionrelation, Eq. (25), for the roughness under study and also for thesmooth duct (6.1% average deviation) as predicted from Eqs. (19)and (23). Thus the presented mathematical model can also be uti-lized for the pressure drop and pumping power calculations, i.e. forthe thermo-hydraulic performance prediction based on the netgain defined by Eq. (38).

5.3. Performance plots

Using the mathematical model employed here, a detailedthermo-hydraulic performance study of solar air heater with v-down discrete rib roughness has been carried out by Karwa and

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 0.02 0.04 0.06 0.08

Eff

icie

ncy

ratio

G (kg/sm2)

Fig. 13. Efficiency ratio versus the mass flow rate per unit area of the plate.

35

40

45

50

55

60

65

70

75

80

0 0.01 0.02 0.03 0.04 0.05 0.06

Effi

cien

cy, %

ΔT/I (Km2/W)

G = 0.01

0.02

0.06

0.050.03

0.04

Re

Thermal efficiencyEffective efficiency

e/dh = 0.07e/dh = 0.06e/dh = 0.05e/dh = 0.04e/dh = 0.03e/dh = 0.02Smooth

Fig. 14. Performance plots of solar air heaters with 60� v-down discrete rectangular rib roughness (L ¼ 2 m, H ¼ 10 mm, εp ¼ 0.95, b ¼ 45� , Ta ¼ 283 K, hw ¼ 5 W m�2 K�1 andI ¼ 800 W m�2) [16].

0

5

10

15

20

25

30

35

40

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Pum

ping

pow

er, W

e/Dh = 0.07e/Dh = 0.02Smooth

G (kg/sm2)

Fig. 15. Pumping power versus the flow rate per unit area of the absorber plate.

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955952

Chauhan [16] for a wide range of operating and ambient parame-ters. The results are available in the form of plots of thermal andeffective efficiencies versus the temperature rise parameter DT/I,which is reproduced here as Fig. 14. The plots in the figure refer tofixed values of L ¼ 2 m, H ¼ 10 mm, L/H ¼ 200, εp ¼ 0.95, b ¼ 45�,Ta ¼ 283 K, hw ¼ 5Wm�2 K�1 and I ¼ 800Wm�2. The plots for thesmooth duct air heater have also been incorporated for a compar-ison with the roughened duct air heaters. The Reynolds numberranges from 2120 to 13,305. For the roughened air heaters, theroughness Reynolds number ranges from about 10 to 75.

It can be seen from the plots in Fig. 14 that, at the lowmass flowrates, the roughened duct air heaters have significantly higherthermal and effective efficiencies as compared to a smooth ductsolar air heater. As explained earlier, this enhancement is the resultof the increased heat transfer coefficient due to the artificialroughness on the absorber plate leading to a higher heat collectionrate and lower absorber plate temperature and hence reduced heatloss from the collector.

It is to note that, at low flow rates (G less than about0.025 kg s�1 m�2), the thermal and effective efficiency values differmarginally only because of the very small pumping powerrequirement at low flow rates (the pumping power PfG3) as canalso be seen fromtheplots of requiredpumpingpower as function ofthe air mass flow rate per unit area of the absorber plate forthe roughened (e/Dh¼ 0.02 and 0.07) and smooth duct air heaters inFig. 15. This also explains the reason for increasing deviationof the effective efficiency curves from those of the thermal efficiencywith increasing flow rate G. It is to note that the pumping poweris also proportional to the friction factor. Hence, the deviationas mentioned above is more significant for collectors with higherrelative roughness height due to the high value of friction factorfor such roughness. At lower flow rates, both thermal and effectiveefficiencies for collectors with relative roughness height e/Dh¼ 0.07

are higher than for the smooth collector or collector with roughnessof low rib roughness heights. For G > 0.03 kg s�1 m�2, this trend ofthe effective efficiency reverses. The roughened duct air heaters arehaving practically the same effective efficiency as that of smoothduct air heater at G z 0.045 kg s�1 m�2. Beyond this flow rate, thesmooth duct air heater is better in thermo-hydraulic performancethan any of the roughened duct air heaters under discussion for thecollector duct depth considered for these plots.

At all flow rates, the pumping power requirement for theroughened duct air heater is greater than that for a smooth duct

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 953

collector due to the greater value of the friction factor for suchducts. Thus, when pumping power is of concern, roughened ductair heaters may be used for mass flow rate G � 0.04 kg s�1 m�2

corresponding to the temperature rise parameter DT/I � 0.015, i.e.,a temperature rise requirement of about 12 �C and higher whensolar insolation value is 800Wm�2. It can be seen that, at the lowerflow rates, the performance of roughened solar air heater havingthe highest value of relative roughness height is better. However, ifpumping power is not of concern, the collector with highest rela-tive roughness height may be selected for all conditions of opera-tions. One such situation can be the replacement of existing smoothduct solar air heater with roughened one where the fan or blowercapacity is under-utilized.

The use of performance plots of Fig. 14 is quite simple. Forexample, let the required temperature rise is 20 �C when solarinsolation is 800 W m�2. The temperature rise parameter (DT/I)works out to be about 0.025. A vertical line on the graph from DT/I z 0.025 cuts the plots for e/Dh ¼ 0.07 at G z 0.026 kg s�1 m�2

with thermal efficiency of about 64.8% and effective efficiency ofabout 63.3%.

The plots of Fig. 14 refer to fixed values of geometrical andambient parameters as mentioned earlier. However, these param-eters vary in actual operation and different designs of the solar airheater with the same roughness may be developed. The effect ofvariation of these parameters on the performance of the roughenedduct collector has also been explained by Karwa and Chauhan [16],which is presented below in brief to highlight the main results oftheir study.

Table 3Effect of change of different parameters on thermal and effective efficiencies; one paramehw ¼ 5 W m�2 K�1 and I ¼ 800 W m�2 [16].

G (kg s�1 m�2) e/Dh A. Duct height, H

H (mm) Dh/h (%) Dhe/h

0.02 0.03 20 �11.45 �105 6.48 1

0.06 0.03 20 �4.26 105 2.19 �122

0.01 0.07 20 �12.88 �125 7.40 6

0.06 0.07 20 �3.57 205 1.83 �194

G (kg s�1 m�2) e/Dh C. Collector slope, b

b (deg) Dh/h (%) D

0.02 0.03 0 �0.40 �0.06 0.03 0 �0.20 �0.01 0.07 0 �0.64 �0.06 0.07 0 �0.20 �G (kg s�1 m�2) e/Dh E. Solar insolation, I

I (W m�2) Dh/h (%)

0.02 0.03 1000 0.50500 �2.3

0.06 0.03 1000 0.97500 �3.01

0.01 0.07 1000 �0.01500 �1.66

0.06 0.07 1000 0.98500 �3.03

G (kg s�1 m�2) e/Dh G. Emissivity of plate, εp H. Combin

εp Dh/h (%) Dhe/he (%) εp

0.02 0.03 0.1 11.0 10.74 0.10.06 0.03 0.1 5.40 6.34 0.10.01 0.07 0.1 15.35 15.38 0.10.06 0.07 0.1 5.13 6.53 0.1

The results of variation of different design, ambient and oper-ating parameters are reproduced in Table 3. The effects have beengiven as relative change in thermal efficiency (Dh/h) and effectiveefficiency (Dhe/he), where h and he are efficiencies at design andoperating parameter values mentioned for the plots in Fig. 14.

The duct depth is a strong parameter affecting both thermal andeffective efficiencies as seen in part (A) of Table 3.

It can be seen that, for the collectors with L/H ¼ 200, effect ofvariation of ambient temperature, slope and length on thermalefficiency is of the order of �1.5% with respect to the result pre-sented in Fig. 14 while the effect of variation in the solar insolationis about 1e3%.

The thermal efficiency of the roughened air heater may reduceby 4e7% when the wind heat transfer coefficient changes from 5 to20 W m�2 K�1 as seen in the table. For collectors with selectivecoating (emissivity of 0.1) on the absorber plate surface, the in-crease in thermal and effective efficiencies is reported to be of theorder of 5e15% and 6e15%, respectively, as given in the table.

From Table 3(H), it can be seen that the effect of wind heattransfer coefficient on solar air heater with selective coating is notsignificant as the presented result is not different from the valuesgiven in part (G) of the table, which depicts the effect of change ofemissivity only. Hence, such collectors may be considered wherethe average wind velocity is high.

The mathematical model presented here has been validatedagainst the experimental data. Looking to the uncertainty in theestimate of certain parameters used in themathematical model, theagreement in the predicted and experimental thermal efficiency

ter has been varied at a time from L ¼ 2 m, H ¼ 10 mm, εp ¼ 0.95, b ¼ 45� , Ta ¼ 283 K,

B. Duct length, L (L/H ¼ 200)

e (%) L (m) H (mm) Dh/h (%) Dhe/he (%)

.89 4 20 0.923 0.95

.25 1 5 �1.04 �1.08

.70 4 20 �0.59 �0.135

.8 1 5 0.2 �0.42

.74 4 20 �0.54 �0.52

.18 1 5 �1.42 �1.43

.09 4 20 �0.6 0.382

.0 1 5 0.51 �0.69

D. Wind heat transfer coefficient, hw

he/he (%) hw (W m�2 K�1) Dh/h (%) Dhe/he (%)

0.42 20 �3.84 �3.870.25 20 0.07 0.080.62 20 �6.88 �6.870.26 20 0.17 0.20

F. Ambient temperature, Ta

Dhe/he (%) Ta (K) Dh/h (%) Dhe/he (%)

0.64 273 0.84 0.90�2.74 303 �0.91 �1.034.62 273 0.16 1.43

�13.98 303 +0.33 �2.020.019 273 1.23 1.25

�1.74 303 �1.96 �1.996.69 273 0.13 2.13

�20.24 303 0.40 �3.42

ed effect of emissivity, εp and wind heat transfer coefficient, hw

hw (W m�2 K�1) Dh/h (%) Dhe/he (%)

20 10.21 10.2720 6.58 7.7320 12.75 12.7920 6.40 8.13

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955954

results of both smooth and roughened duct solar air heaters isreasonably good. Hence, the model can be utilized for the perfor-mance prediction of both smooth duct air heater and air heaterwith v-down discrete rib roughness under different flow, geometricand ambient parameter values.

6. Conclusions

Results of the experimental study of thermal efficiency for bothsmooth duct solar air heater and air heater with v-down discrete ribroughness have been compared with the predicted values from amathematical model to validate the presented model. The standardand average deviations of the predicted and experimental data ofthermal efficiency are about�11% and 8%, respectively. The reasonsfor the deviations have been identified as the uncertainties in theestimates of the wind heat transfer coefficient, heat transfer co-efficients and sky temperature from the available correlations.

The enhancement in the thermal efficiency due to artificialroughness on the airflow side of the absorber plate has been foundto be 12.5e20% depending on the flow rate; higher enhancement isat the lower flow rate, which is attributed to the enhancement inthe heat transfer coefficient due to the employment of theroughness.

The plate temperature excess (mean temperature of the plateover the ambient temperature) for the roughened absorber plate issignificantly lower (18.5e40.8 K) than the smooth duct (33e53.2 K), which clearly indicates a lower operating temperature andhence increased thermal efficiency due to the reduced heat lossfrom the roughened duct solar air heater compared to the smoothduct air heater.

The experimental friction factor results have been found to be inreasonable agreement with the predicted data for both theroughened (5.7% average deviation) and smooth duct (6.1% averagedeviation) from the predicted values from the equations given inthe mathematical model. Thus the presented mathematical modelcan be used for the thermo-hydraulic performance prediction.

The results of a detailed thermo-hydraulic performance study ofsolar air heater with v-down discrete rib roughness using themathematical model validated here are available in the form ofplots of thermal and effective efficiencies from an earlier study,which has been reproduced here. The results of the study regardingthe effect of variation of various parameters on the predicted col-lector performance have also been reproduced.

Nomenclature

A absorber plate area ¼ WL, m2

Ap aperture area of collector, m2

Ae area of the edge of collector rejecting heat to ambient, m2

Ao area of orifice in the orifice plate, m2

B/S relative roughness length of discrete rib elementsCd coefficient of dischargecp specific heat of air, J/kg KDh hydraulic diameter of duct ¼ 4WH/[2(W þ H)], me rib height, meþ roughness Reynolds numbere/Dh relative roughness heightf Fanning friction factorg heat transfer functionG mass flow rate per unit area of plate ¼ m/A, kg/s m2

Gr Grashoff numberG1 mass velocity ¼ m/WH, kg/s m2

h heat transfer coefficient, W/m2 KH airflow duct height (depth), m

hpg the convective heat transfer coefficient between theabsorber plate and glass cover, W/m2 K

hw wind heat transfer coefficient, W/m2 KI solar radiation on the collector plane, W/m2

k thermal conductivity of air, W/m Kkg thermal conductivity of glass, W/m Kki thermal conductivity of the insulation, W/m KL length of collector, mm mass flow rate, kg/sNu Nusselt numberp rib pitch, mP pumping power, Wpa atmospheric pressure, N/m2

Pr Prandtl number ¼ mcp/kp/e relative roughness pitchq heat flux ¼ Q/A, W/m2

Q useful heat gain, WQb heat loss from back, WQe heat loss from edge, WQtg conduction heat transfer through the glass, WQtpg heat transfer by radiation and convection from absorber

plate to inner surface of glass cover, WQtga heat transfer by radiation and convection to ambient from

outer surface of glass cover, WQL overall heat loss rate, WR roughness functionRa Rayleigh numberRe Reynolds number ¼ G1Dh/mSt Stanton number ¼ Nu/RePrTa ambient temperature, KTfm, Tm mean air temperature, KTi inlet air temperature, KTmpg mean of the plate and glass temperatures ¼ (Tp þ Tgi)/2, KTo outlet air temperature, KTpm mean plate temperature, KTsky sky temperature, KUL overall loss coefficient, W/m2 KVw wind speed, m/sW width of the duct, mw width of the rib, mm

Greek symbolsa angle of attack, absorptivityb collector slope, degd thickness of insulation, mmdg thickness of glass, mmdpg gap between the absorber plate and glass cover, mDp pressure drop, N/m2

DT air temperature rise ¼ To � Ti, KDh change in thermal efficiencyDhe change in effective efficiencyε emissivityh thermal efficiencyhe effective efficiencym dynamic viscosity, Pa snmpg kinematic viscosity of air at temperature Tmpg, m2/ssa transmittanceeabsorptance product.

Subscriptsb duct bottom surfaceg glassm meanp plate

R. Karwa, G. Chitoshiya / Energy 55 (2013) 939e955 955

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