Performance of packed bed solar air heater

Solar Energy 74 (2003) 319–329

H eat transfer and friction factor correlations for packed bedsolar air heater for a low porosity system

a b , b*N.S. Thakur , J.S. Saini , S.C. SolankiaDepartment of Mechanical Engineering, National Institute of Technology, Hamirpur (H.P.) -177005 (H.P.), India

bDepartment of Mechanical and Industrial Engineering, I.I.T. Roorkee, Roorkee 247667,India

Received 11 October 2001; accepted 21 April 2003

Abstract

An experimental investigation has been carried out on a low porosity packed bed solar air heater. This investigation coversa wide range of geometrical parameters of wire screen matrix, i.e. wire diameter 0.795 to 1.40 mm, pitch 2.50 to 3.19 mmand number of layers from 5 to 12. The correlations have been developed for the Colburnj factor and friction factor for alow range of porosities from 0.667 to 0.880 and packing Reynolds number range from 182 to 1168. It is observed that boththe heat transfer coefficient and the friction factor are strong functions of geometrical parameters of the porous packed bed.A decrease in porosity increases the volumetric heat transfer coefficient. 2003 Elsevier Ltd. All rights reserved.

1 . INTRODUCTION volumetric heat transfer coefficient for packed bed thermalstorage systems. Their results revealed that the volumetric

A solar air heater is a simple device to heat air by heat transfer coefficient is generally higher for beds withutilizing solar energy. It finds applications in drying lower porosities. With this important point in mind, aagricultural products, such as seeds, fruits, vegetables and critical review of literature in the area of heat transfer inin space heating as a low temperature energy source. packed beds was carried out with particular emphasis onSeveral designs of solar air heaters with different configu- the effect of bed porosity on the volumetric heat transferration such asChiou et al. (1965) and Hamid and coefficient.Beckman (1971)have been proposed to enhance the Basic research on convective heat transfer from screensthermal performance of a solar air heater. There is a was performed byCoppage and London (1956), Tong andsignificant interest in a packed bed solar air heater becauseLondon (1957), Kays and London (1964)and Hamid andof some exclusive advantages of such a system over a Beckman (1971).Flow resistance in screens was measuredconventional system. The packed bed solar air heater byWieghardt (1953). Chiouet al. (1965) and Chiou andabsorbs the solar radiation ‘in depth’ and has a higher ratio El-Wakil (1966)proposed the use of a porous bed made ofof heat transfer area to volume and a high heat transfer a slit and expanded aluminium foil matrix and a wirecoefficient. Several experimental studies in the past have screen matrix for a packed bed solar air heater. Theyattempted to obtain detailed information on the heat studied the heat transfer and flow friction characteristicstransfer mechanism by using the porous packings in the air for a high porosity range from 0.962 to 0.983.ducts (Chiou and El-Wakil, 1966; Chiouet al., 1965; Varshney and Saini (1998)have experimentally investi-Coppage and London, 1956; Tong and London, 1957). The gated the heat transfer and the fluid flow characteristics ofmain objective of these studies was to determine the a solar air heater having its duct packed with wire mesh

screen matrices (air flowing parallel to matrix planes). Awide range of geometrical parameters of wire screenmatrix with wire diameter 0.360 to 0.795 mm, pitch from2.08 to 3.19 mm and number of layers from 5 to 14 havebeen used. They developed the heat transfer and the*Author to whom correspondence should be addressed.

E-mail address: [email protected](J.S. Saini). friction factor correlations for air flowing through the bed

0038-092X/03/$ – see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0038-092X(03)00153-1

mailto:[email protected]

320 N.S. Thakur et al. / Solar Energy 74 (2003) 319–329

Nomenclature

2A Heat transfer area (m )2A Frontal area (m )f

21a Specific surface area per unit volume (m )v

b , b , b , b , b , b Coefficients used in Eqs. (14)–(16) and (18), respectively1 2 3 4 5 6

c Specific heat of air (J /kg K)p

d Diameter of M.S. pipe used with orifice plate (m)1

d Wire diameter of wire screen matrices (m)w

D Depth of rectangular duct (m)D Hydraulic diameter (m)h

f Average friction factor for packed bedp

f Average friction factor for conventional ductc2G Relative mass flow rate (mass velocity) of air in the duct (kg/s m )o

2h Average heat transfer coefficient (W/m K)h Volumetric heat transfer coefficient,h av v

2 / 3j Colburn j factor for packed bed, St Prh p

j Colburn j factor for conventional collectorhc

k Thermal conductivity of air (W/m K)L Length of collector (m)m Mass flow rate (kg/s)m , m , m , m Slope of the line1 2 3 4

m , m Slope of the line5 6

n Number of layersQ Heat transfer rate (W)Nu Nusselt number for conventional collector duct,hD /kh

Nu Nusselt number for packed bed, 4r h /kp h2

DP Pressure drop in the duct (N/m )P Pitch of wire mesh screen (m)t

Pr Prandtl number,mc /kp

P Porosity of bedr Hydraulic radius, Pd /4(12P)h w

Re Reynolds number for conventional duct,ruD /mh

Re Reynolds number of packed bed, 4r G /mp h o

St Stanton number of packed bed,h /c Gp p o

St Stanton number for conventional collector,h /urcc p

t Average air temperature (8C)fm

t Inlet air temperature (8C)i

t Average matrix temperature (8C)pm

t Average outlet temperature (8C)o

u Velocity of air in the duct, (G /r)o3V Volume of packed bed, m

Std. error Standard errorC.V. Coefficient of variation in %

2r Dependence or coefficient of determinationGreek letters

2m Dynamic viscosity of air, N s/m

3r Density of air, kg/mh Efficiency index Eq. (22)

N.S. Thakur et al. / Solar Energy 74 (2003) 319–329 321

in the cross flow arrangement (cross flow here means the systems have been extensively investigated for heat trans-airflow is perpendicular to the direction of solar insola- fer and fluid flow characteristics, a system formed bytion). The range of packing Reynolds number and porosity packing a rectangular duct (of solar air heater) with wirecovered in these experiments was from 300 to 1500 and mesh screens representing a flow system parallel to the0.89 to 0.96, respectively. The following correlations have screens has not been investigated except that byVarshneybeen developed. and Saini (1998)for relatively high porosity systems. In

view of this, experimentation was planned for investigating2.104P1 heat transfer and fluid flow characteristics of packed bedt 20.55] ]j 50.647 S D Re (1)F S DGh p solar air heaters with packing density for a low porositynP dw

range. The details of the experimental work and the results0.699P1 are presented next.t 20.44] ]f 5 2.484 S D Re (2)F S DGp pnP dw

It has been observed that there is a general increase in2 . EXPERIMENTAL SET-UPvolumetric heat transfer coefficient as porosity decreases.

The above review of the literature shows that there is a The experimental set-up used in the present inves-substantial rise in the volumetric heat transfer coefficient tigation, as shown inFig. 1, was designed, fabricated,with a decrease in porosity and hence a lower porosity installed and used for data collection on heat transfer andsystem would be a better candidate when one looks for the fluid flow characteristics of solar air heaters with packedenhancement of performance of a solar air heater utilizing bed and without packed bed. It consisted of a test sectiona packed bed in its duct. Further, although packed bed having two identical ducts, one smooth duct (like that in a

Fig. 1. Schematic diagram of experimental set-up.


solar air heater in common use) and the other one similar enabled measurement of the bulk mean temperature at thein size but provided with a packed bed using wire screen outlet of the test section. The length of the exit section wasmatrices. Both the ducts had an identical length of 2.40 m 0.5 m (L /D 510.6) and the cross section area matchedh

(L /D 551), width of 0.40 m, and depth of 0.025 m with that of the test duct. Three equally spaced baffleh

(having D 50.047 m) and were made of softwood, both plates which spread over 100 mm length beyond the exith

inclined at an angle of 208 to the horizontal. The smooth section were provided for the purpose of mixing the hot air(or conventional) duct had an absorber plate of 2 mm coming out of the solar collectors to obtain a uniformaluminium sheet. It was blackened with black board paint temperature of the air at the outlet. The mixing section wason the side facing solar radiation. It had a 3 mm thick glass connected to the Mild Steel pipe fitting through a transitionsheet cover fixed 20 mm above the absorber plate. The piece and flexible pipes. A 2.2 kW (3.0 h.p.) centrifugalsides and bottom of the duct were insulated with thermocol blower was used for drawing air through the duct.sheet. (Thermocol is a commercial insulation of foamed Calibrated orifice plates, one in each were used topolystyrene having a thermal conductivity 0.037 W/m/K). measure the airflow rates in both the ducts. The orificeThe reason for using two ducts in the present set-up was to plate arrangement was designed for the flow measurementcompare the performance at the same operating conditions in the pipe of inner diameter of 78 mm, as per thesuch as mass flow rate, insolation and inlet fluid tempera- recommendation ofPreobrazhensky (1980).The orificeture. plate was fitted between the flanges, so aligned that it

The packed bed duct had a 2 mm aluminium sheet remained concentric with the pipe. The length of thehaving several layers of wire mesh screens arranged one straight mild steel pipe provided was based on a pipeabove the other on the upper side of the aluminium sheet diameterd , which is the minimum of 10d on the1 1

while below it there was 50 mm of thermocol and 12 mm upstream side and 5d on the down streamside of the1

plywood. The sides were made of softwood, 25 mm thick. orifice plate as recommended byEhlinger (1950).IS 2952A glass cover was provided on the upper side which rested (Part—1) 1964 also recommends using upstream andon batons fixed adjacent to the side wall at a height of downstream straight lengths withL /D ratios of 20 and 6,25 mm. Another glass cover was fixed at a height of respectively, taking into account the disturbances created20 mm above the first one and supported on the frame, by baffles, transition section and blower. In the presentleaving a stagnant air gap of 20 mm between the two glass experimental set-up theL /D ratio is 30 on the upstreamcovers. Flow straighteners were provided on the inlet side side of the orifice and is 6 on the downstream side. Thisof the test ducts to enable the flow to stabilize. These were longer length on the upstream side is provided to accountmade of softwood having the same cross sectional area as for disturbances due to transition and baffles. A standardthat of the test section. The length of the straightener was set of inlet and outlet pressure taps were provided at a0.9 m (L /D 519.1) in accordance with the design consid- distance of 25.4 mm on each side of the orifice plate.Fig.h

erations (Varshney and Saini, 1998). A wooden exit 2 shows the dimensions of the packed bed, the locations ofsection was provided at the outlet of the test duct which pressure taps, and the layout of thermocouples. Thewas followed by a mixing device, namely baffles for temperature distribution in the bed and temperature of themixing the air. The exit section reduced the effect of air at the inlet and outlet of the test section were measuredsudden change on the test section. The mixing device by means of pre-calibrated copper constantan thermocou-

Fig. 2. Details of the packed bed collector.


ples. A digital micro-voltmeter was used to indicate the matrices were placed between the back plate and the loweroutput of the thermocouples in8C. The temperature cover glass in the packed bed solar air heater duct. Quasi-measurement system was calibrated to yield temperature steady-state readings of the temperature of the wire screenvalues (t60.1)8C. The pressure drop across the test section at various locations, plate temperature, inlet and outletwas measured by using a calibrated micro-manometer. temperature of the air, pyranometer readings for intensity

The entry length provided before the test section was of solar radiation and micro-manometer readings forreally not a conventional flow straightener but was added pressure drop across both the ducts as well as across thefor the purpose of flow stabilization as air entered from the orifice meters were, recorded at half hour intervals. Beforeatmosphere to the duct. The swirling flows induced due to starting the experiment, all joints between the duct, inletthe centrifugal fan, baffles and Y-configuration of the section, mixing device and pipefittings were carefullyset-up are very important. Although the detailed effect of examined for leakage. All the joints, where there wasswirl has not been investigated, however it can be stated possibility of any leakage, were sealed by using putty.with confidence that this effect will not cause a large Data pertaining to a given specific flow rate correspondingpercentage of error in the results shown by the comparison to a clear sky day were recorded between 10.45 a.m. andof the data collected for smooth duct with respect to 1.45 p.m. While recording the temperatures the ice bath,Nusselt number and friction factor. This comparison was selector switch, lead wire joints and micro-voltmeter werecarried out in the form of validation of experimental set-up protected from direct solar radiation. It was ensured thatas given below. the cold junction of the thermocouple always remained in

contact with melting ice. Experimental data were collectedfor five sets of matrices, with seven runs each for different

23 . VALIDATION OF EXPERIMENTAL SET-UP mass flow rates ranging between 0.01 to 0.03 kg/s m . Thedetails of the geometrical parameters including porosity of

Before collecting the data from the experimental set-up, all the matrices tested are given inTable 1.the system was tested for validity by experimentation on asmooth duct (one of the two ducts provided) to determinethe Nusselt number and the friction factor. These values of

5 . PROCESSING OF EXPERIMENTAL DATAthe Nusselt number and the friction factor were comparedwith those obtained from the (Dittus and Boelter) correla-

The experimental data was used to determine the desiredtion and Blasius equation given in (Bhatti and Shah, 1987).

parameters as given below. All the properties of air, viz.The Nusselt numbers have a maximum deviation of 4.24%

density, viscosity, specific heat, Prandtl number used in thewhile the maximum deviation of the friction factor is

calculation, were evaluated at the arithmetic mean of the1.78% from the predicted values by the (Dittus and

inlet and the outlet temperature of air.Boelter) correlation and Blasius equation, respectively.

The heat transfer rate,Q to the air can be determined as:This gave confidence in the data collected with the set-upand instrumentation used especially indicating that the Q 5mc (t 2 t ) (3)p o i

effect of the swirling flow induced baffles, transition andblower was not significant and the leakage is negligibly The average heat transfer coefficient,h, between thesmall. wire screens matrix and air was based on the following

equation.

Q4 . EXPERIMENTAL PROCEDURE]]]h 5 (4)A t 2 ts dpm fm

After satisfactory calibration of instruments and valida-tion of the experimental set-up, blackened wire screen where,t , is the average temperature of the measurementspm

T able 1Geometrical parameters of wire screen matrices

Matrix Dia. of Pitch Number Bed depth Bed Heat transfer Pitch to wire Hydraulic Surface area per3designation wire (d ) (P ) of layers (D) porosity area (A) dia. ratio radius (r )3 10 unit volume (a )w t h v

2 21(mm) (mm) (n) (mm) (P) (m ) P /d (m) (m )t w

A 1.05 2.50 12 25.0 0.667 30.44 2.38 0.525 12691

A 1.05 2.50 10 25.0 0.722 25.41 2.38 0.681 10592

A 1.05 2.50 8 25.0 0.778 20.29 2.38 0.919 8453

A 1.40 3.00 5 25.0 0.820 12.40 2.14 1.590 5144

A 0.79 3.19 9 25.0 0.880 14.49 4.01 1.450 6045


made along the length and depth of the packed bed whereDp is the pressure drop across the duct andwhereas,t , is the average air temperature.fm GoThe volumetric heat transfer coefficient was determined ]u 5 (13)

ras:

h 5 h 3 a (5)v v

6 . ERROR ANALYSISwhere,a , is the heat transfer area per unit volume of thev

bed (5 A /V ). A uncertainty or error analysis was carried out as per theThe heat transfer area,A, was determined from the procedure widely used in the literature, viz. the method

frontal area,A , porosity P and wire diameter,d , as:f w suggested byKline and McClintock (1953).The uncertain-ty estimates obtained are given below at 95% confidence4A L(12P)f

]]]]A5 (6) leveldw

The porosity of the matrix was determined by following Mass flow rate,m 61.62% odd 20 in 1the procedure ofTong and London (1957)using the Heat gain,Q 61.73% odd 20 in 1geometrical parameters of the bed matrix. Reynolds number, Re 63.68% odd 20 in 1p

The Reynolds number Re for the packed bed duct was Heat transfer coefficient,h 62.70% odd 20 in 1p

calculated using the hydraulic radius,r , relative mass flow Vol. heat transfer coefficient,h 63.60% odd 20 in 1h v

rate (mass velocity)G , and viscosity coefficientm, as Colburn j factor, j 63.39% odd 20 in 1o h

Friction factor, f 63.68% odd 20 in 1p4r Gh o]]Re 5 (7)p m

The hydraulic radiusr , for the packed bed ducts is theh 7 . COMPARISON OF PRESENT EXPERIMENTALratio of void volume to wetted surface area and was RESULTS WITH THE AVAILABLE RESULTScalculated asVarshney and Saini (1998).

A typical set of experimental results was compared inPdw]]]r 5 (8)h Fig. 3 with the values of j-factor obtained from the4(12P)

correlations proposed byCoppage and London (1956),The hydraulic radiusr is related both to the packing Tong and London (1957), Handley and Heggs (1968)andh

size and the void space. Choice of this parameter (r ) as Varshney and Saini (1998).A considerably large differ-h

the characteristic length in the wire screen matrices has ence can be seen inFig. 3 which shows that the existingbeen discussed in detail byWhitaker (1972).For the same correlations cannot be used for the prediction of heatreason, this parameter (r ) has been used traditionally by a transfer results for systems using low porosity wire meshh

number of researchers, viz.Coppage and London (1956),Tong and London (1957), Kays and London (1964)and

Varshney and Saini (1998).The relative mass flow (mass velocity),G is given by:o,

m]]G 5 (9)o (A )Pf

The value of heat transfer coefficient was used todetermine the Stanton number andj factor, respectively,as:

h]]Stanton number St5 (10)p G co p

2 / 3Colburn j factor j 5St (Pr) (11)h p

Using the pressure drop data, the friction factor,f , wasp

calculated as follows

Dp]r S Dh L]]]f 5 (12)p 2

ru Fig. 3. Comparison of present experimental results with existing]

correlation.2


beds with wire mesh oriented parallel to the air flow asused in the solar air heater ducts.

8 . RESULTS AND DISCUSSION

8 .1. Variation of volumetric heat transfer coefficient (h )v

Based on the experimental data, the variation of volu-metric heat transfer coefficienth , with Reynolds numberv

for different matrices is shown inFig. 4. It was observedthat the value of heat transfer coefficient increased with theincrease in Reynolds number. The intensity of turbulencewas higher at higher Reynolds number resulting in a highervolumetric heat transfer coefficient. This behavior wasobserved for all the matrices. It can also be observed fromFig. 4 that the value of volumetric heat transfer increasedmonotonically with a decrease in porosity; the porositydecreased from A to A . This appears to be due to a Fig. 5. Effect of Reynolds number on Colburnj factor for5 1

higher level of turbulence created in the flow as the different matrices.porosity decreased and the flow passages become moretortuous and narrower with a higher solidity of such m1j 5 b (Re ) (14)h 1 psystems.

The value of coefficientsb and m differ from matrix1 1

8 .2. Variation of Colburn j factor ( j ) to matrix, showing them to be functions of the bedh

geometrical parameters, the slopem varying between1

The heat transfer data have also been presented in the20.594 to20.619 depicting only a very slight variation.form of a non-dimensional relationship, the Colburnj An arithmetic mean value ofm , i.e. 20.61 can beh 1

2 / 3(defined asj 5St Pr ). The variation of this factor with selected to represent the characteristics of all these ma-h p

Reynolds number shown inFig. 5 can be represented by a trices. Using this mean value ofm for all matrices, the1

relation of the following form on the log log scale using values of coefficientb were determined. It was observed1

the linear regression. that the straight line on the log–log scale represented theabove empirical relation. The values ofb , which differed1

from matrix to matrix, are given inTable 2(a) and associated uncertainties in the value ofm andb are given1 1

in Table 2(b).

8 .3. Effect of porosity

The porosity depends on a complex relationship of thegeometrical parameters like wire diameter, pitch, numberof layers in the given depth of bed. The same porosity maybe produced by different combinations of geometricalparameters. The flow pattern of air through matriceshaving different pitch, wire diameter, and number of layersin a fixed bed depth can be different even if the porosity isthe same. Thus besides the porosity, the number of layersin a given depth of bed and the pitch to wire diameter ratio

T able 2(a)Value of coefficientb for different matrices (m 520.61 for all1 1

matrices)

Matrix A A A A A1 2 3 4 5

Fig. 4. Effects of Reynolds number on volumetric heat transferCoefficientb 0.1377 0.1420 0.1547 0.2000 0.16001coefficient for different matrices studied.


T able 2 (b)Uncertainties in the values ofm and b at 95% confidence level1 1

Matrix Parameter Value Std. error C.V. % Dependence

A m 20.6100 0.0175 2.80 0.991 1

b 0.1370 0.0136 9.90 0.991

A m 20.6100 0.0087 1.40 0.992 1

b 0.1420 0.0072 5.07 0.991

A m 20.6100 0.0121 1.90 0.993 1

b 0.1547 0.0113 7.30 0.991

A m 20.6100 0.0061 1.00 0.994 1

b 0.2000 0.0082 4.10 0.991

A m 20.6100 0.0096 1.57 0.995 1

b 0.1600 0.0100 6.25 0.991

P /d will be important parameters which affect the flow for all values of the ratio of pitch to wire diameter. Thet w

behaviour as reported byVarshney and Saini (1998).The relation is given below:similarity of the trend of parametric dependence ofj factor

m 0.472j 1 1hand friction factor as for the experimental results of ]] ] ]5 b S D 50.37S D (15)220.61 nP nPVarshney and Saini (1998)revealed that an analogous Rep

correlating relationship could be developed for the presentexperimental results. The values of coefficientb and power index (exponent)2

m and associated uncertainties at 95% confidence level2

8 .4. Development of correlation were determined. The standard error in the power indexwas 0.0180 and coefficient of variation was 3.85%, and for

Keeping the above discussion in mind, a plot between coefficientb the standard error was 0.130 and coefficient220.61( j /Re ) vs. (1 /nP)(P /d ) is drawn inFig. 6. From of variance was 3.51%.h p t w

the plot it is clear that the points are scattered and hence Similarly a log–log plot between the parameterJ /h20.61the relationship as such is not applicable. The associated Re and pitch to diameter ratio (P /d ) yielded, afterp t w

uncertainties are also given inFig. 6. linear regression, following relation. The values of parame-20.61A relationship betweenj /Re and 1/nP was de- ter and associated uncertainties were also determined ath p

termined from a log–log plot and linear regression analysis 95% confidence levels. The standard error and coefficient

20.61 20.61 0.50 0.25Fig. 6. Plot betweenj /Re and (1/nP)(P /d ) for all ma- Fig. 7. A plot betweenj /Re and (1/nP) (P /d ) for allh p t w h p t w

trices. matrices.


T able 3 (a)of variance in the power index and the coefficientb are3Values of coefficientb for different matrices (m 5 20.41 for all0.010 and 4.3%, and 0.012 and 10%, respectively. 5 5

matrices)m 0.253j P Ph t t Matrix A A A A A]] ] ]5 b 50.12 (16) 1 2 3 4 5S D S D320.61S D d dRe w wp Coefficientb 1.45 1.50 1.59 1.90 1.655

0.50 0.25The [(1/nP) (P /d ) ] is taken one parameter and at w20.61 0.50 0.25

20.41 0.50 0.25plot betweenJ /Re versus (1/nP) (P /d ) ash p t w Re and (1/nP) (P /d ) as shown inFig. 9. Thep t wshown inFig. 7 was prepared. It is interesting to note that relationship that represents the data points satisfactorilya single straight line (on a log–log scale) can well well can be given below and associated uncertainties arerepresent data in the form of the following equation. also shown in the figure at 95% confidence level.

m0.250.50 4P1 t 20.61 m0.250.50 6] ]j 5 b S D Re (17) P1F S D Gh 4 p t 20.41nP d ] ]f 5 b S D Re (20)w F S D Gp 6 pnP dw0.25 1.40.50 P1 t 20.61] ]j 50.4 S D Re (18) 0.25 0.90F S D G 0.50h p P1nP d t 20.41w ] ]f 5 3.0 S D Re (21)F S D Gp pnP dwA similar procedure was followed for the development

of a correlation for the friction factor.Fig. 8 shows the plot The comparison between experimental values ofj factorfor the friction factorf , as a function of Reynolds number,p and friction factor with the values predicted by theRe for different matrices. The friction factors for differentp corresponding correlating Eqs. (18) and (21) was made inmatrices in terms of Reynolds number can be represented Figs. 10 and 11.It was observed that all the predictedby a general relation of the following form. values for thej factor lay within the maximum deviation of

m 10.5% (and 97% of data points lies within66%) whereas5f 5 b (Re ) (19)p 5 pthe maximum deviation of friction factor was 7% (and94% data points lay within the65.98%) of the experimen-where b is a function of geometrical parameter. The5

tal values. Further, the comparison of the results obtainednumerical value of coefficientb for all matrices is given5

from Eqs. (18) and (21) with those obtained from thein Table 3(a) and associated uncertainties are given incorresponding Eqs. (1) and (2) developed byVarshney andTable 3(b).Saini (1998)were also made and presented inFig. 12. ItIt is expected that the coefficientb is a function of5

0.50 0.25 can be seen that the results predicted by the present(1/nP) (P /d ) as in the case of the Colburnjt w

correlation were much closer to experimental results asfactor.compared to those of Varshney and Saini correlations.Based on this analogy a plot was drawn betweenf /p

Further, it is important to note that the enhancement ofheat transfer as a result of using packed beds is accom-

panied by a considerable enhancement of friction losses.This results in considerably large additional pumpingcosts. Consequently any enhancement scheme must beevaluated on the basis of consideration of pumping costs.A well-known method of such evaluation is that proposedby Webb (1994)in the form of an efficiency index,h ,e

defined by the following equation.

fj ph] ]h 5 Y . (22)S D S De j fhc c

For an enhancement scheme to be viable, the value ofthis index must be greater than unity. In the range ofparameter investigated in this work, the value of this indexwas found to lie between 1.14 and 1.58 while the enhance-ment of heat transfer in terms of the ratio of thej factor,j /j , was found to lie between 1.25 and 1.83. Therefore ith hc

can be concluded that this system of enhancement repre-sents a suitable scheme from the point of view of addition-al pumping power penalty as judged by a parameter calledFig. 8. Effect of Reynolds number on friction factor for all

matrices. ‘efficiency index,h ’ being sufficient greater than 1.0.e


T able 3 (b)Uncertainties in the values ofm and b at 95% confidence level5 5

Matrix Parameter Value Std. error C.V. % Dependence

A m 20.410 0.0199 4.85 0.991 5

b 1.4500 0.0158 1.09 0.995

A m 20.410 0.01405 3.42 0.992 5

b 1.500 0.1226 8.17 0.995

A m 20.410 0.0078 1.90 0.993 5

b 1.590 0.0757 4.76 0.995

A m 20.410 0.0130 3.17 0.994 5

b 1.900 0.0147 7.17 0.995

A m 20.410 0.0131 3.19 0.995 5

b 1.650 0.1409 8.52 0.995

9 . CONCLUSIONS

It can be concluded that a considerable enhancement ofheat transfer can be obtained from the packed bed solar airheater by lowering the value of porosity of the bed. Thisenhancement is a function of bed geometrical and oper-ating parameters. Based on the experimental data collectedin this work, correlations for low porosity range of 0.667to 0.880 and Reynolds number range of 182 to 1168, havebeen developed for thej factor and the friction factor,which correlated the experimental data satisfactorily. Themaximum deviations between the experimental results andthose predicted by the correlations for thej factor and theh

friction factor were 10.5 and 7%, respectively. It has alsobeen found that this method of heat transfer enhancementwas a suitable scheme from the point of view of additionalpumping power penalty.

Fig. 10. Comparison between experimental and predicted valuesof j .h

20.41 0.5 0.25Fig. 9. A plot betweenf /Re and (1/nP) (P /d ) for all Fig. 11. Comparison between experimental and predicted valuesp p t w

matrices. of friction factor.


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Performance of packed bed solar air heater