Heat transfer and friction factor correlations for impinging jet solar air heater

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Heat transfer and friction factor correlations for impinging jet solar air heater

Ranchan Chauhan ⇑, N.S. ThakurCentre for Energy and Environment, NIT Hamirpur, HP, India

a r t i c l e i n f o

Article history:Received 27 June 2012Received in revised form 19 September 2012Accepted 23 September 2012Available online 3 October 2012

Keywords:Jet impingementSolar air heaterNusselt numberFriction factor

a b s t r a c t

Experimental investigation has been carried out to study heat transfer and friction factor characteristicsusing impinging jets in solar air heater duct. The effect of flow and geometrical parameters, especially thejet diameter, streamwise and spanwise pitch has been studied. The experiments encompassed the flowReynolds number in the range 3800–16,000. The jet diameter, streamwise pitch and spanwise pitch eachnormalized by hydraulic diameter of the duct are in the range: 0.043–0.109; 0.435–1.739; 0.435–0.869respectively. The air through the jets is impinged normally onto the absorber surface which was heatedwith uniform heat flux of 1000 W/m2. The heat transfer and friction factor data obtained is comparedwith that of parallel flow solar air heater under similar geometrical and flow conditions. The results showthat there is considerable enhancement in heat transfer and friction factor by 2.67 and 3.5 times respec-tively. Correlations for Nusselt number and friction factor have been developed in terms of above param-eters which reasonably correlate the experimental data.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

The Solar air collector has an important place among solar ther-mal systems as it is widely used in many commercial applicationssuch as to supply hot air to buildings, agricultural and industrialdrying [1] etc. The thermal efficiency of solar air heaters is gener-ally low because of low convective heat transfer coefficient be-tween the absorber plate and the moving fluid (air) whichincreases the absorber plate temperature leading to higher heatlosses to the ambient, resulting in low thermal efficiency of suchcollectors [2]. To increase the thermal performance of such collec-tors heat has to be transferred efficiently. Studies have reportedthat a directed fluid released against the heat transferring surfacecan efficiently transfer large amount of thermal energy and massbetween the surface and the fluid. Compared with conventionalconvection cooling by confined flow parallel to (under) the cooledsurface, jet impingement produces heat transfer coefficients thatare up to 3 times higher as the impingement boundary layers aremuch thinner and often the spent fluid after impingement servesto turbulate the surrounding fluid. Also the flow required froman impinging jet device for a required heat transfer coefficientmay be two orders of magnitude smaller than that required for acooling approach using free wall parallel flow [3].

Impingement with high velocity gas jets is an established meth-od of convectively heating/cooling in a wide variety of processesand thermal control applications. The major application of imping-

ing jets includes solar heat absorbers [4], turbine blades [5], micro-electro-mechanical component [6], etc. Researchers in heat trans-fer field are interested in studying the thermal performance ofmulti-jet impingement cooling where improved performance sig-nificantly prolongs the operating life of the aforementioned com-ponents. The characteristics of multiple jet impingements areinfluenced basically by two types of interactions. Firstly, the inter-ference between the adjacent jets can be before impingement onthe surface. This may happen when the distance between the jetsin small and/or when the distance between the jet plate and targetsurface is large. Secondly, the wall jets formed by the adjacent jetscollide on the target surface. Such interactions are possible whenthe pitch is small and/or when the distance between the jet plateand target surface is small but jet velocity is large. The effects ofchanging impingement plate geometric and flow parameters at rel-atively low speeds are considered in variety of existing publica-tions. The effects of Reynolds number and streamwise/spanwisejet spacing at low speed impingement cooling are addressed byKercher and Tabakoff [7], Chance [8], etc. Metzger et al. [9] pre-sented heat transfer characteristics measured on a target surfacebeneath a two dimensional array of impinging jets at low speedindicate that in-line arrangement of jets provide better heat trans-fer than staggered arrangements. Florscheuetz et al. [10] includesdata on channel crossflow mass velocity in addition to correlationwhich gives Nusselt number dependence on these parameters aswell as on jet impingement plate geometry, prandtl number andReynolds number. Brevet et al. [11] considered a row of impingingjets in a test section in which the spent air was constrained to exitin single direction. Effects of Reynolds number, impingement

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⇑ Corresponding author. Tel.: +91 9418011870; fax: +91 1972223834.E-mail address: [email protected] (R. Chauhan).

Experimental Thermal and Fluid Science 44 (2013) 760–767

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distance and spanwise jet-to-jet spacing on Nusselt number distri-bution lead to recommendation for optimum Z/D of 3–6 and opti-mal spanwise jet spacing of 4–5 jet diameters.

It is of utmost importance in solar thermal collectors to ensure ahigh average rate of heat transfer across the entire surface. As thecrossflow can significantly lower the overall heat transfer in jetimpingement cooling [12] an impingement based heat transfer insolar air heaters should incorporate exit from one direction. Byvarying the flow and geometric parameters, including the number,size and spacing of the jet orifices, the potential exists for adjust-ment of the heat transfer coefficients to achieve a specified distri-bution in surface temperature or heat flux. It appears that theknowledge of the effects of array configuration on heat transferand friction characteristics has been inadequate for achievementof optimum designs for solar air heaters. The application of jetimpingement to solar air collectors involves low flow Reynoldsnumber. More appropriate studies have been conducted byKercher and Tabakoff [7] and by Kuroda and Nishioka [13] bothof whom carried out experimental investigations on heat transferat low Reynolds number, but these studies did not provided anyinformation regarding friction losses occurring inside the ductresulting in increase in pumping power penalty. Most recent studycarried out by Belusko et al. [14] to study the performance of jetimpingement in unglazed air collectors reported 21% increase inthermal efficiency. Although the study did not report heat transferand friction characteristics of the impinging jet solar air heater.Thus, the present investigation has been carried out with the pri-mary objective of determining the heat transfer behavior for arange of uniformly spaced array configurations for interest in solarair heating energy systems. Also the previous studies reported onlyheat transfer correlations but in case of solar air heaters it is impor-tant to evaluate friction losses inside the rectangular duct in orderto evaluate that by what percentage the solar air heater is costeffective. Thus, the measurement of heat transfer and pressuredrop across the test section as a function of flow rate and geomet-rical parameters has been carried out with the objective of devel-oping a correlation for Nusselt number and friction factor whichwould be of direct use to the designer. The correlation for Nusseltnumber and friction factor are correlated in terms of Reynolds

number and in terms of three geometrical parameters: the stream-wise jet spacing, the spanwise jet spacing and jet diameter eachnormalized by hydraulic diameter of the rectangular duct (X/Dh,Y/Dh,Dj/Dh). The range of parameters is presented in Table 1.

2. Experimental details

2.1. Experimental test facility

A schematic layout of the experimental set up is shown inFig. 1a. The experimental test set up has been designed andfabricated to study the effect of jet impingement on the absorbersurface through circular jets in a duct flow of solar air heater.The test set up consists of entrance section, test section, exitsection, orifice meter and the suction blower at the other end.The rectangular duct measures 2.4 � 0.29 � 0.025 m with testsection of 1.4 m, entry and exit lengths of 0.6 m and 0.4 m respec-tively. The entry and exit lengths are chosen as per ASHRAEStandards [15] which recommends entry length P 5

pWZ and exit

length P 2.5p

WZ for the turbulent flow regime. A uniform heatflux is provided by an electric heater, fabricated by loops ofnichrome wire of size 1.4 m � 0.29 m located on top wall of thetest section with other sides insulated. A variable transformer isconnected to maintain a specific voltage and an ammeter to mea-sure the current flowing through the circuit in order to maintainuniform heat flux of 1000 W/m2. A mica sheet of 0.5 mm thicknessis sandwiched between the nichrome wire and the asbestos sheetof 5 mm thickness to prevent back heating from the heater thuspreventing top loss. In order to prevent heat loss to surroundingsthe whole periphery of the rectangular duct is covered by 76 mmglass wool on top and 50 mm wooden blocks from other sides ofthe duct. The mass flow rate of air through the duct is measuredby using a calibrated orifice meter fitted between two flangedpipes of suitable length to keep the orifice plate concentric withthe pipe and U-tube manometer filled with isopropyl alcohol.The pressure drop across the test section has been measured bya micro-manometer with least count of 0.01 mm of Hg. The tem-peratures at various locations are measured by calibrated K-Typethermocouples (0.3 mm i.e. 24 SWG) to indicate the average tem-perature of air at inlet and outlet and at 15 locations on the absor-ber plate as shown in Fig. 1b. The impingement plate is inserted inthe rectangular duct in between absorber plate which is the heattransferring surface and the base plate to produce jets for impinge-ment, normally onto the absorber surface. The rectangular duct isso designed so that the impingement test plates can be installedat the location. Fig. 1c shows the location of streamwise and span-wise pitch on the impingement test plate. A suction blower is fixedat the other end to draw the air into the rectangular duct, and the

Nomenclature

Ap surface area of absorber plate (m2)Ao area of orifice meter (m2)Cd coefficient of dischargeCp specific heat of air (J/kg K)Dj diameter of jet (m)Dh hydraulic diameter of duct (m)f friction factorh heat transfer coefficient (W/m2 K)L length of the test section (m)Nu Nusselt numberDPo pressure drop across orifice plate (Pa)DP pressure drop across test section (Pa)Qu useful heat gain (W)

Re reynolds numberTfi temperature of fluid at inlet (K)Tfo temperature of fluid at outlet (K)Tfm mean temperature of flowing fluid (K)Tpm mean temperature of absorber plate (K)W width of the duct (m)X streamwise pitch (m)Y spanwise pitch (m)Z height of the duct (m)

Greek symbolsq density (kg/m3)b ratio of orifice diameter to pipe diameter

Table 1Range of flow and geometrical parameters.

Reynolds number, ‘‘Re’’ 3800–16,000Streamwise pitch to hydraulic diameter ratio, ‘‘X/Dh’’ 0.435–1.739Spanwise pitch to hydraulic diameter ratio, ‘‘Y/Dh’’ 0.435–0.869Duct aspect ratio, ‘‘W/Z’’ 11.6Jet diameter to hydraulic diameter ratio, ‘‘Dj/Dh’’ 0.045–0.109

R. Chauhan, N.S. Thakur / Experimental Thermal and Fluid Science 44 (2013) 760–767 761


air flow rate was maintained using air valves fixed at inlet and exitof the blower as shown in Fig. 1a. The impingement flow which is-sues from these holes is contained within the channel formed bythe impingement jet plate and the target plate, and is constrainedto exit in a single direction.

2.2. Experimental procedure and range of parameters

The experimental data pertaining to heat transfer and flow fric-tion was collected in accordance with recommendation of ASHRAEStandard 93-97 [15] for testing of solar collectors. In the presentstudy 48 jet impingement test plates with different values of jetparameters were investigated in addition to the smooth parallelflow under same conditions for the purpose of comparison withimpinging jet plates. The jet plate was inserted in between the backplate and the target (absorber) plate and the set up was checked for

air leakage if any before each set of experimentation. The blowerwas switched ON to let a predetermined rate of air inflow in theduct. The absorber plate was then heated with the electric heaterfabricated to produce uniform heat flux of 1000 W/m2 and placedover the test section of the absorber plate. Six values of air flowrates were used for each set at same or fixed uniform heat flux.At each value of the air flow rate and the corresponding heat flux,the system was allowed to attain a steady state before the data wasrecorded. The steady state was assumed to be achieved when noconsiderable variations of temperatures between successive scanswas observed for 10–12 min. During experimentation the follow-ing parameters were measured for each set of readings:

1. Temperature of the absorber plate (Tpm).2. Temperature of air at inlet (Tfi) and outlet (Tfo) of the test

section.3. Pressure drop across the test section (DP).4. Pressure difference across the orifice plate to measure air flow

rate (DPo).

The range of parameters covered in the present study is as givenin Table 1.

2.3. Data reduction

The experimental data obtained was used to compute heattransfer rate, Nusselt number and friction factor in order to deter-mine the effect of jet impingement on heat transfer and friction

Fig. 1a. The schematic layout of experimental set up.

Fig. 1b. Location of thermocouples on absorber plate.

Fig. 1c. Impingement plate geometry: Location of streamwise and spanwise pitch.

762 R. Chauhan, N.S. Thakur / Experimental Thermal and Fluid Science 44 (2013) 760–767


characteristics in solar air heater duct. Mass flow rate ( _m), heattransfer from absorber plate to the flowing fluid (Qu), heat transfercoefficient (h) and Nusselt number (Nu) in the duct were calculatedas:

The mass flow rate of air determined from the pressure dropacross the orifice plate using following relation:

_m ¼ CdAo2qair;0DPo

1� b4

� �0:5

ð1Þ

The useful heat gain of air is calculated as

Q u ¼ _mCpðTfo � TfiÞ ð2Þ

The heat transfer coefficient for the test section is

h ¼ Q u

ApðTpm � TfmÞð3Þ

Nusselt number is calculated as

Nu ¼ hDh

Kð4Þ

The friction factor was determined from the measured values ofpressure drop across the test length, L = 1.4 m using followingrelation:

f ¼ DPDh

2qairLV2air

ð5Þ

The thermophysical properties of air used in the calculationswere obtained from a text by Duffie and Beckman [16] correspond-ing to mean bulk temperature of air (Tfm).

By using the estimation method of Kline and McKlintock [17],the maximum uncertainty of heat transfer coefficient, h is±2.29%. The individual errors contributed to the uncertainty of hfor the measured and physical properties are: Mass flow rate:±1.73%, velocity of air in the duct: ±1.78%, useful heat gain:±2.23%. The maximum uncertainties of other non-dimensionalparameters are Reynolds number: ±2.19%, Nusselt number:±2.42% and friction factor: ±3.06%.

3. Validity tests

The validity tests have been carried out to serve as a basis ofcomparison of results with the values of Nusselt number and fric-tion factor from the correlations available in the literature for thesmooth rectangular duct.

The Nusselt number for smooth rectangular duct is given byDittus–Boelter equation [18] as

Dittus—Boelter equation : Nus ¼ 0:023Re0:8Pr0:4 ð6Þ

The friction factor for a smooth rectangular duct is given bymodified Blassius equation [19] as

Blassius equation : fs ¼ 0:085Re�0:25 ð7Þ

The comparison of experimental and predicted values ofNusselt number and friction factor as a function of Reynoldsnumber has been shown in Figs. 2 and 3 respectively. The averageabsolute deviation of the present experimental Nusselt numberdata is 3.53% from the values predicted by Eq. (6) and averageabsolute deviation of friction factor data is 2.08% from thevalues predicted by Eq. (7). This shows a good agreement betweenexperimental and predicted values, which ensures the accuracy ofthe experimental data collected for investigation.

4. Results and discussion

The experimental data obtained is used to study the heat trans-fer, friction factor discussed in following subsections.

4.1. Heat transfer and friction factor

Fig. 4 shows Nusselt number variation with jet diameter tohydraulic diameter ratio (Dj/Dh) at different values of Reynoldsnumber. The values of Nusselt number were found to increase withincreasing Reynolds number as expected. As Reynolds numberincreases, thickness in boundary layer decreases due to decreasein convective resistance and thus the heat transfer increases. Thejet diameter to hydraulic diameter ratio of 0.065 yield maximumvalue of Nusselt number at all values of Reynolds number. TheNusselt number beyond this value showed substantial decreasein heat transfer. The variation of friction factor with that of varyingDj/Dh has been plotted in Fig 5. It was observed that the maximumvalue of friction factor was obtained at jet diameter to hydraulicdiameter ratio of 0.043 and minimum value at 0.109 for the rangeof parameters studied.

The variation of Nusselt number with Reynolds number for dif-ferent values of streamwise pitch to hydraulic diameter ratio (X/Dh) and fixed Dj/Dh of 0.065 is as presented in Fig. 6 which showsthat very low heat transfer is achieved at X/Dh of 0.435 and in-creases as the streamwise pitch increases to maximum of 1.739.Nusselt number was found to be increased with increase in

Reynolds Number, Re2000 4000 6000 8000 10000 12000 14000 16000 18000

Nus

selt

Num

ber,

Nu

0

10

20

30

40

50

60

Experimental ValueDittus Boelter Eqn.

Fig. 2. Comparison of experimental and predicted values from Dittus–Boelterequation.

Reynolds Number, Re2000 4000 6000 8000 10000 12000 14000 16000 18000

Fric

tion

Fact

or, f

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016Experimental ValueBlasius Equation

Fig. 3. Comparison of experimental and predicted values from Blasius equation.



Reynolds number for each of the case as expected. Increase in Rey-nolds number results in increase in the turbulence which increasesthe heat transfer through the duct. Also, increase in the streamwisepitch ratio (X/Dh) resulted in decrease in interference of adjacentjets before impinging on the absorber plate and thus high heattransfer is achieved. From Fig. 6 it can be seen that increase inReynolds number and streamwise pitch ratio there is significant

enhancement in the values of Nusselt number as compared tothe conventional parallel flow solar air heater. However, increasein heat transfer through impinging jets also results in increase infriction factor. The effect of Reynolds number on friction factorfor different values of streamwise pitch ratios has been plotted inFig. 7 which represents decrease in friction factor values with in-crease in Reynolds number in all the cases as expected. As the fric-tion factor decreases with increase in Reynolds number andincreases with increase in streamwise pitch ratio, the maximumvalue of friction factor has been observed at X/Dh of 1.739. Thestreamwise pitch ratio was restricted by the friction penalty (f/fs)so that the performance parameter may be kept within acceptablelimits. Likewise streamwise pitch ratio, the spanwise jet locationsalso influence the heat transfer through the rectangular duct of so-lar air heater. The spanwise pitch ratio (Y/Dh) studied in the range0.435–0.869 represents that increase in pitch between adjacentrows yields increased Nusselt number values as the jet to jet inter-ference decreases as jet to jet pitch length increases. The variationof Nusselt number with that of spanwise pitch ratios at differentReynolds numbers has been plotted in Fig. 8 with other parametersfixed which shows that increasing row to row pitch results in heattransfer enhancement although there is low heat transfer enhance-ment compared to streamwise pitch ratio. The friction factor vari-ations for different spanwise pitch ratios as presented in Fig. 9show that there is increase in friction factor as spanwise pitch ratioincreases. The spanwise pitch ratio of 0.435 represents the lowestvalues of friction factor and increases for Y/Dh value of 0.625 and

Jet diameter to hydraulic diameter ratio, Dj/Dh

0.02 0.04 0.06 0.08 0.10 0.12

Nus

selt

num

ber,

Nu

0

20

40

60

80

100

120 Re = 16000Re = 14100Re = 11000Re = 8100Re = 5700Re = 3800

X/Dh = 0.435 Y/Dh = 0.435

Fig. 4. Variation of Nusselt number as a function of jet diameter ratio (Dj/Dh).

Jet diameter to hydraulic diameter ratio, Dj/Dh

0.02 0.04 0.06 0.08 0.10 0.12

Fric

tion

fact

or, f

0.005

0.010

0.015

0.020

0.025

0.030

0.035 Re = 3800Re = 5700Re = 8100Re = 11000Re = 14100Re = 16000

X/Dh = 0.435Y/Dh = 0.435

Fig. 5. Variation of friction factor as a function of jet diameter ratio (Dj/Dh).

Reynolds number, Re2000 4000 6000 8000 10000 12000 14000 16000 18000

Nus

selt

num

ber,

Nu

0

20

40

60

80

100

120

140X/Dh = 0.435X/Dh = 0.869X/Dh = 1.304 X/Dh = 1.739Parallel flow

Y/Dh = 0.869Dj/Dh = 0.065

Fig. 6. Variation of Nusselt number as a function of Reynolds number.

Streamwise Pitch Ratio, X/Dh

0.5 1.0 1.5 2.0

Fric

tion

Fact

or, f

0.00

0.02

0.04

0.06

0.08Re = 3800Re = 5700Re = 8100Re = 11000Re = 14100Re = 16000

Y/Dh = 0.869Dj/Dh = 0.065

Fig. 7. Variation of friction factor as a function of streamwise pitch (X/Dh).

Spanwise Pitch, Y/Dh

0.4 0.6 0.8 1.0

Nus

selt

Num

ber,

Nu

20

40

60

80

100

120

140

160

180Re = 3800Re = 5700Re = 8100Re = 11000Re = 14100Re = 16000

X/Dh = 1.739 Dj/Dh = 0.065

Fig. 8. Variation of Nusselt number as a function of spanwise pitch ratio (Y/Dh).



0.869. However difference in increase in friction factor value from0.435 to 0.625 is more than from 0.625 to 0.869 because there isalmost no interference between the adjacent jets before strikingat the absorber surface due to increase in spanwise jet to jetdistance.

The flow through solar air heater duct using impinging jetsshows considerable enhancement in heat transfer. Fig. 10 repre-sents enhancement in Nusselt number in terms of enhancement ra-tio (Nu/Nus) which is greater than unity for all values of Reynoldsnumber with maximum value of 2.67 at Dj/Dh of 0.065. This is dueto decrease in interference between adjacent jets prior to impinge-ment which results in formation of thin boundary layer in the vicin-ity of heat transferring surface. The region where the jet strikesexhibits higher heat transfer than that of parallel flow due to turbu-lence generated by the shear between wall jet and surrounding fluidwhich is then transported to the boundary layer at heat transferringsurface. The variation of friction factor ratio with Reynolds numberis represented in Fig. 11 and is 3.5 times than that of smooth duct atthe point where Nusselt number is maximum.

4.2. Correlations for Nusselt number and friction factor

From Figs. 4–9 it can be concluded that Nusselt number andfriction factor are strong functions of flow and geometric parame-ters, namely Reynolds number (Re), streamwise pitch ratio (X/Dh),spanwise pitch ratio (Y/Dh) and jet diameter to hydraulic diameterratio (Dj/Dh). Therefore, the functional relationship for Nusseltnumber and friction factor can be written as

Nu ¼ fnðRe; X=Dh;Y=Dh;Dj=DhÞ

f ¼ fnðRe; X=Dh;Y=Dh;Dj=DhÞ

The data corresponding to all impingement test plates totaling288 data points were used for regression analysis. In order todetermine the functional relationship between Nusselt numberand Reynolds number the plot of ln (Nu) as a function of ln (Re)is plotted as shown in Fig. 12. A regression analysis to fit a straightline through these data points is:

Nu ¼ AoRe0:8512 ð8Þ

The constant Ao in Eq. (8) will be a function of other geometricparameters i.e. streamwise pitch to hydraulic diameter ratio (X/Dh),so Nu/Re0.8512 = Ao is plotted on log–log scale as shown in Fig. 13 asa function of streamwise pitch to hydraulic diameter ratio (X/Dh)and by regression analysis it was obtained as:

NuRe0:8512 ¼ BoðX=DhÞ0:1761 ð9Þ

Further, the constant Bo will be a function of other influencingparameters. Considering spanwise pitch to hydraulic diameter ra-tio (Y/Dh), the values of Nu

Re0:8512 ¼ 0:02337ðX=DhÞ0:1761 ¼ Bo are plot-ted in Fig. 14 as a function of (Y/Dh) on log–log scale and fromthe regression analysis through these points, following wasobtained:

Spanwise Pitch, Y/Dh

0.4 0.5 0.6 0.7 0.8 0.9

Fric

tion

fact

or, f

0.02

0.04

0.06

0.08Re = 3800Re = 5700Re = 8100Re = 11000Re = 14100Re = 16000

X/Dh = 1.739 Dj/Dh = 0.065

Fig. 9. Variation of friction factor as a function of spanwise pitch (Y/Dh).


Enha

ncem

ent r

atio

, Nu/

Nu s

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2Dj/Dh = 0.043Dj/Dh = 0.065Dj/Dh = 0.087 Dj/Dh = 1.109

X/Dh = 1.739Y/Dh = 0.869

Fig. 10. Variation of enhancement ratio with Reynolds number.


Fric

tion

fact

or ra

tio, f

/f s

2

4

6

8 Dj/Dh = 0.043Dj/Dh = 0.065Dj/Dh = 0.087Dj/Dh = 0.109

X/Dh = 1.739Y/Dh = 0.869

Fig. 11. Variation of friction factor ratio with Reynolds number.

ln (Re)8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8

ln (N

u)

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

Nu = Ao Re0.8512

Fig. 12. Plot of ln (Nu) as a function of ln (Re) for all the experimental values.



Nu

Re0:8512ðX=DhÞ0:1761 ¼ CoðY=DhÞ0:141 ð10Þ

where Co is a function of parameter representing ratio of diameterof jet to hydraulic diameter of the rectangular duct. Finally a plot

of ln NuRe0:8512ðX=DhÞ0:1761ðY=DhÞ0:141

h i¼ Co as a function of Dj/Dh as shown

in Fig. 15 has been used to fit on log–log scale through these points,given as:

lnNu

Re0:8512ðX=DhÞ0:1761ðY=DhÞ0:141

" #

¼ ln Do þ D1 lnðDj=DhÞ þ D2ðlnðDj=DhÞÞ2 ð11Þ

Rearranging Eq. (11) and substituting respective values ob-tained by regression analysis, finally yields the following correla-tion for Nusselt number.

Nu ¼ 1:658� 10�3Re0:8512ðX=DhÞ0:1761ðY=DhÞ0:141ðDj=DhÞ�1:9854

� exp½�0:3498ðlnðDj=DhÞÞ2 ð12Þ

Fig. 16 shows the plot of experimental values and the valuespredicted using Eq. (12). The data relevant to this correlation is:

(a) Average absolute deviation: 3.21%.(b) Regression coefficient: 0.98.(c) Values of constants Ao, Bo, Co, Do, D1, D2 are 0.0273, 0.02337,

0.0292, �6.4021, �1.9854, �0.3498 respectively.

A similar procedure has been employed and a correlation forfriction factor has been developed. The correlation for friction fac-tor is in the following form:

f ¼ 0:3475Re�0:5244ðX=DhÞ0:4169ðY=DhÞ0:5321ðDj=DhÞ�1:4848

� exp½�0:2210ðlnðDj=DhÞÞ2� ð13Þ

Fig. 17 shows the comparison of measured values and the val-ues predicted using Eq. (13). The data relevant to this correlationis:

(a) Average absolute deviation: 5.96%.(b) Regression coefficient: 0.98.(c) Values of constants A11, B11, C11, D11 are 3.2217, 0.59191,

3.852, 0.3475.

Thus, the correlations developed are satisfactory for the predic-tion of Nusselt number and friction factor of an impinging jet solarair heater with fairly good accuracy in the range of investigatedparameters. From Eqs. (12) and (13) it can be seen that Reynoldsnumber has much stronger effect on Nusselt number than on fric-tion factor compared to other parameters investigated. Also,streamwise pitch spacing have much stronger effect on Nusseltnumber than spanwise pitch ratio. Another notable difference liesin the effect of ratio of jet diameter to hydraulic diameter of theduct, the influence on friction factor is where decreasing due to in-crease in jet diameter ratio, on Nusselt number the effect isincreasing up to Dj/Dh of 0.065 and decreases thereafter as furtherincrease leads to formation of stagnation region very near to the

ln (X/Dh)-1.0 -0.5 0.0 0.5 1.0

ln {N

u/R

e0.85

12}

-4.2

-4.0

-3.8

-3.6

-3.4

-3.2

Nu = Bo Re0.8512 (X/Dh)0.1761

Fig. 13. Plot of ln {Nu/Re0.8512} = ln (Ao) as a function of ln (X/Dh).

ln (Y/Dh)-1.0 -0.8 -0.6 -0.4 -0.2 0.0

ln {N

u/[R

e0.85

12 (X

/Dh)

0.17

61]}

-4.0

-3.8

-3.6

-3.4Nu = Co Re0.8512 (X/Dh)

0.1761(Y/Dh)0.141

Fig. 14. Plot of ln {Nu/[Re0.8512(X/Dh)0.1761]} = ln (Bo) as a function of ln (Y/Dh).

ln (Dj/Dh)-3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0

ln {N

u/[R

e0.85

12 (X

/Dh)

0.17

61(Y

/Dh)

0.14

1 ]}

-3.9

-3.8

-3.7

-3.6

-3.5

-3.4

-3.3

Nu = Do Re0.8512 (X/Dh)0.1761(Y/Dh)0.141(Dj/Dh)-1.9854

X exp[-0.3498{ln(Dj/Dh)}2]

Fig. 15. Plot of ln {Nu/[Re0.8512(X/Dh)0.1761(Y/Dh)0.141]} = ln (Co) as a function of ln(Dj/Dh).

Nu (experimental)20 40 60 80 100 120 140

Nu

(pre

dict

ed fr

om c

orre

latio

n)

20

40

60

80

100

120

-9%

+9%

Fig. 16. Comparison of experimental and predicted values of Nusselt number.



impingement plate and the tendency of high velocity jets to ap-proach the impingement surface prior to interference with the sur-rounding jets decreases and thus results in lower heat transferenhancement. Fig. 18 exhibits the variation of Nusselt number ob-tained at different jet diameters with Reynolds number, in whichcomparison of the present study and the work carried out byKercher and Tabakoff [7] and Miao et al. [20] is presented. In thefigure, the calculation was carried out at jet diameter of 3 and5 mm which shows increase in Nusselt number with increase inReynolds number.

5. Conclusions

An experimental study of the flow of air through the holesimpinging normally on the absorber surface in a solar air heaterhas been performed. The effect of Reynolds number, geometricalparameters i.e. streamwise pitch, spanwise pitch, jet diameter eachnormalized by hydraulic diameter of the duct, on heat transfer andfriction factor has been studied. The investigation covered aReynolds number range of 3800–16,000. The results of the studyare compared with that of smooth duct under similar flow condi-tions and the following conclusions are drawn:

(a) The streamwise and spanwise pitches have strong effect onthe formation of impingement boundary layer and henceon the performance of impinging jet solar air heater. An

appreciable heat transfer enhancement has been obtained.Maximum enhancement in Nusselt number is of the orderof 2.67 and correspondingly the friction factor is 3.5 times.

(b) The maximum enhancement in Nusselt number at Dj/Dh of0.065 has been obtained beyond which the interferenceeffects increases and thereby decreases heat transferperformance.

(c) The high heat transfer coefficient achieved is due to the thinimpingement boundary layers generated in the vicinity ofthe heat transferring surface. The impinging jets afterimpingement serve to turbulate the surrounding fluid andthus improve performance of solar air heater. The heattransfer enhancement obtained in the present case is ataffordable pumping power requirements.

(d) Based upon the experimental values, statistical correlationsfor Nusselt number and friction factor have been developedin terms of investigated parameters with average absolutedeviation of 3.21% and 5.96% which reasonably correlatethe experimental data.

References

[1] N.K. Bansal, Solar air heater applications in India, Renew. Energy 16 (1999)618–623.

[2] M.A. Wazed, Y. Nukman, M.T. Islam, Design and fabrication of a cost effectivesolar air heater for Bangladesh, Appl. Energy 87 (2010) 3030–3036.

[3] N. Zuckerman, N. Lior, Jet impingement heat transfer: physics, corrrelationsand numerical modeling, Adv. Heat Transfer 39 (2006) 565–631.

[4] M. Roger, R. Buck, H.M. Steinhagen, Numerical and experimental investigationof a multiple air jet cooling system for application in solar thermal receiver,ASME J. Heat Transfer 127 (2005) 682–876.

[5] J.C. Han, Recent studies in turbine blade cooling, Int. J. Rotating Machinery 10(2004) 443–457.

[6] K.S. Myung, M. Issam, Experimental and numerical investigation of singlephase heat transfer using a hybrid jet impingement/micro-channel coolingscheme, Int. J. Heat Mass Transfer 49 (2006) 682–694.

[7] D.M. Kercher, W. Tabakoff, Heat transfer by a square array of round air jetsimpinging perpendicular to a flat surface including the effect of spent air,ASME Trans. J. Eng. Power 92 (1970) 73–82.

[8] J.L. Chance, Experimental investigation of air impingement heat transfer underan array of round jets, TAPPI 57 (1974) 108–112.

[9] D.E. Metzger, L.W. Florschuetz, D.I. Takeuchi, R.D. Behee, R.A. Berry, Heattransfer characteristics for inline and staggered arrays of circular jets withcrossflow of spent air, ASME Trans. J. Heat Transfer 101 (1979) 526–531.

[10] L.W. Florschuetz, C.R. Truman, D.E. Metzger, Streamwise flow and heat transferdistribution for jet array distributions for jet array impingement withcrossflow, ASME Trans. J. Heat Transfer 103 (1981) 337–342.

[11] P. Brevet, C. Dejeu, E. Dorignac, M. Jolly, J.J. Vullierme, Heat transfer to a row ofimpinging jets in consideration of optimization, Int. J. Heat Mass Transfer 45(2002) 4191–4200.

[12] K. Garret, B.W. Webb, The effect of drainage configuration on heat transferunder an impinging liquid jet array, J. Heat Transfer 121 (1999) 803–810.

[13] H. Kuroda, K. Nishioka, Heat transfer in a channel with uniform injectionthrough a perforated wall, J. Heat Transfer 111 (1989) 182–185.

[14] M. Belusko, W. Saman, F. Bruno, Performance of jet impingement in unglazedair collectors, Solar Energy 82 (2008) 389–398.

[15] ASHARE Standard 93–97, Method of Testing to Determine the ThermalPerformance of Solar Collector, 1977.

[16] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, Wiley, NewYork, 1974.

[17] S.J. Kline, F.A. McClintock, Describing uncertainties in single sampleexperiments, Mech. Eng. 75 (1953) 3–8.

[18] W.H. Kays, H. Perkin, Forced Convection Internal Flow in Ducts, McGraw Hill,New York, 1990.

[19] M.S. Bhatti, R.K. Shah, Turbulent and Transition Convective Heat Transfer inDucts, Wiley, New York, 1987.

[20] J.M. Miao, C.Y. Wu, P.H. Chen, Numerical investigation of confined multiple jetimpingement cooling over a flat plate at different crossflow orientations,Numer. Heat Transfer Part A: Appl. 55 (2009) 1019–1050.

f (experimental)0.00 0.02 0.04 0.06 0.08

f (pr

edic

ted

from

cor

rela

tion)

0.00

0.02

0.04

0.06

0.08

-12%

+12%

Fig. 17. Comparison of experimental and predicted values of friction factor.


Nus

selt

num

ber,

Nu

20

40

60

80

100

120 Miao et al. [20] Dj = 5mmKercher and Tabakoff [7] Dj = 5mmPresent study Dj = 5mmKercher and Tabakoff [7] Dj = 3mmPresent study Dj = 3mm

Fig. 18. Comparison of Nusselt number at different Reynolds number.


Heat transfer and friction factor correlations for impinging jet solar air heater

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