head transfer and friction factor inside elliptic tubes

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JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 3, 023110 �2011�

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eat transfer and friction factor inside elliptic tubestted with helical screw-tape inserts

M. Moaweda�

Department of Mechanical Engineering, Faculty of Engineering Shoubra,Benha University, 108 Shoubra Street, Shoubra, Cairo 11689, Egypt

�Received 18 September 2009; accepted 25 March 2011; published online 25 April 2011�

Experimental investigation of heat transfer and friction factor characteristics ofelliptic tubes with different twist ratios �Y� and pitch ratios �S� has been conductedunder laminar flow condition. All data are obtained using cold water flowing in thetube side and hot water flowing in the annuli side of the heat exchanger. Theexperiments covered a range of Reynolds numbers, 5.7�102�Re�1.31�103.Heat transfer and friction factor analyses are presented for different conditions ofRe, S, and Y. The results indicate that the helical screw element of different Y andS has an effect on the results of heat transfer coefficient and friction factor. Theaveraged Nusslet number �Nu� increases with an increase in Re and it decreaseswith an increase in Y and S. For a fixed Reynolds number, the friction factor �f�increases with a decrease in Y and S for the elliptic tubes. The thermal performancefactor �� is introduced to indicate the percentage increase in Nu over the percent-age increase in f . The maximum percentage increase in Nu over the percentageincrease in f �maximum increase in �� is 19.7% and 42.3% at the values of S andY equal to 1 and 0.22, respectively. Correlations of the average Nusselt number andfriction factor with Re, S, and Y are presented. © 2011 American Institute ofPhysics. �doi:10.1063/1.3582940�

. INTRODUCTION

In the past few decades, heat transfer enhancement technology has been developed and widelypplied in many engineering applications. Heating or cooling of viscous liquids in process indus-ries, heating or cooling of oils, heating of circulating fluid in solar collectors, and heat transfer inompact heat exchangers are a few example. Heat transfer augmentation techniques play a vitalole here since heat transfer coefficients are generally low for laminar flow in plain tubes. Insertionf twisted tapes in tubes is one of such augmentation techniques.

Thus, research in this area has captivated the interest of a number of researchers, e.g., Eiamsand Promvonge.1 In passive technique, improvement is acquired without providing any extra flownergy. In compound technique, two or more active or passive techniques may be utilized simul-aneously to produce an enhancement that is much higher than that of the techniques operatingeparately as presented by Yilmaz et al.2,3 Mamer and Bergles4–6 reported experimental data foraminar flows of ethylene glycol with a twisted-tap ratio of 5.39 in an isothermal tube.

Mangilk and Bergles7–9 developed the generalized Nusslet number and friction factor corre-ations. Local convective-condensation measurements for four refrigerant fluids—R134a, R410A,125, and R32—in a microfin tube were presented by Kedzierski and Goncalves.10 Their research

howed that R32 exhibits the highest heat transfer performance due to its high thermal conduc-ivity. The turbulent mixed convection in a horizontal circular tube provided with an inserted stripas been studied by Hsieh et al.11

Al-Fahed et al.12 compared pressure drop and heat transfer coefficients obtained from a plain

�
Author to whom correspondence should be addressed. Electronic mail: [email protected].
3, 023110-1941-7012/2011/3�2�/023110/15/$30.00 © 2011 American Institute of Physics

011 to 182.16.241.33. Redistribution subject to AIP license or copyright; see http://jrse.aip.org/about/rights_and_permissions

http://dx.doi.org/10.1063/1.3582940

http://dx.doi.org/10.1063/1.3582940

http://dx.doi.org/10.1063/1.3582940

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023110-2 M. Moawed J. Renewable Sustainable Energy 3, 023110 �2011�

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icrofin and twisted tape inserted tubes. Sarma et al.13 presented a new approach for predictingonvective heat transfer coefficient of a tube equipped with twisted tape at different pitch toiameter ratios. The predicted results were compared with empirical correlations. Recently, Sarmat al.14 proposed generalized correlations for predicting friction factor and convective heat transferoefficient for twisted tapes in a tube. Reasonable agreement was obtained from comparisonetween the predicted results and the measured data. Several investigations were carried out toetermine the effect of coiled wire or twisted tape elements on heat transfer and friction factor forlong time.15–17 This is because wire coil or twisted tape insert in a tube creates swirling flows

hat modify the near wall velocity profile due to various vorticity distributions in the vortex core.he fluid mixing between the tube core and the near wall region is enhanced because of swirl

nduced tangential flow velocity component. However, accompanied with swirl induced heat trans-er enhancement, the shear stress and pressure drag in a tube with coiled wire or twisted tape insertre increased accordingly. For using compound turbulators, Promvonge and Eiamsa-ard18–20 in-estigated the effects of conical-nozzle, conical-ring, or V-nozzle together with a swirl generatordecaying swirl� on heat transfer and friction characteristics in a uniform heat flux tube and foundhat using both enhancement devices, the increase in heat transfer rate is about 20%–50% of usingsingle enhancement device, but there is also a substantial rise in pressure loss.

A review of a previous work showed that there are no data on heat transfer and friction factornside elliptic tubes fitted with full length helical screw-tape inserts. So, the present paper reportsn the heat transfer and friction factor characteristics of laminar flow through circular and ellipticubes fitted with full length helical screw-tape inserts. Also, correlations based on the data gathereduring this work for predicting heat transfer coefficient and friction factor inside elliptic tubestted with full length helical screw-tape inserts are proposed for practical applications.

I. EXPERIMENTAL APPARATUS

The experimental setup consists of a counterflow double pipe heat exchanger and a water flow

P PTest section

Ball valve

Flaw meter

Flaw meter

Cold water tankPump

Heater

Hot water tankPump

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Flow meter

Flow meter

FIG. 1. Diagram of the experimental setup.

ystem with its accessories. As shown in Fig. 1, hot water circuit is arranged as follows: a hot


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023110-3 Heat transfer J. Renewable Sustainable Energy 3, 023110 �2011�

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ater storage tank that provides multiple electrical heaters with rheostat, a half hp centrifugalump, a flow meter, a piping system with suitable valves, and an inner tube of heat exchanger. Thetorage tank is perfectly insulated by 50 mm layer of glass wool and covered by a galvanized steelheet. The tank is fitted with suction, return, and vent pipes. The vent pipe has two functions: tonsure that the storage tank is filled continuously with water to save heater elements and to preventccumulation of pressure inside the storage tank that may result from temperature rise or backressure. All hot pipes are insulated with suitable insulation thickness and secured with a galva-ized steel cover. Cold water is supplied from city water passing through a calibrated flow metero the inside tube of the heat exchanger. Therefore, cold water flow rate could be changed whileot water flow is constant and controlled using bypass system using a backflow branch and aegulating valve, as shown in Fig. 1.

Two sets of double pipes are used separately in the present experiment as test sections. Therst one is double circular copper tube that has a length of 1500 mm. The inner tube has an inneriameter of 38.1 mm and a thickness of 2 mm, while the outer tube diameter has an inner diameterf 63.5 mm and a thickness of 2 mm. The second one is a double copper elliptic tube with theame surface area as the first one and the same length of 1500 mm. The axis ratiomajor /minor�=2 for both inner and outer tubes with minor axis=24 and 40 mm for inner anduter tubes, respectively. The set of plain double circular tubes is used to compare against therevious work and plain double elliptic tubes. The second set of double elliptic tubes is used withifferent screw-tape inserts inside the inner elliptic tube. The helical screw-tape inserts witharious twist ratios are made by winding uniformly different strips in width over a 5 mm rod andoated with chromium by electroplating to prevent corrosion �Fig. 2�. The twist ratio Y, which isefined as the ratio of width of the strip �w� to the diameter of twist �dst�, is varied from 0.22 to.35 at a constant of pitch ratio �S=1�. The pitch ratio is defined as the ratio of pitch �H� to theiameter of twist �dst� and it ranged from 0.46 to 2.15 at a constant of twist ratio �Y =0.31�. Theuter tube of the heat exchanger is perfectly insulated with a glass wool of 40 mm thick toinimize heat loss.

Nine T-type calibrated thermocouples are inserted into the test section and distributed regu-arly. They are used to measure cold water, hot water, and wall temperature at the inlet, middle,nd exit of the test section, in addition to hot water in the storage tank. The thermocouples arexed in the surface of the tube by making a small notch at a specified location where the junctionf thermocouples is soldered. To get fluid bulk temperatures, groups of thermocouples are fixed at

(a)

b)!

Flow meter

Flow meter

dst

H

w

FIG. 2. �a� Cross section of the elliptic tube. �b� Configuration of the inserted tape.

ifferent locations at the inlet and outlet of cold and hot water. The fluid bulk temperatures at the


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nlet and outlet of cold and hot water are calculated from the average of readings of fixed groupsf thermocouples. All instruments and measurements have certain general characteristics errors,nd uncertainties are inherent in both instrument and process of making the measurement. Theeadings of thermocouples are taken by means of a multichannel digital thermometer with aesolution of 0.1 °C. The pressure drop across the inner tube is measured using pressure taps andigital calibrated manometer. When steady state condition is established, water flow rates, pressurerop, and all thermocouples temperatures have been recorded.

II. UNCERTAINTY ANALYSIS

Generally, the accuracy of the experimental results depends on the accuracy of individualeasuring instruments and manufacture accuracy of elliptic tubes. Also, the accuracy of an in-

trument is limited by its minimum division �its sensitivity�.Based on uncertainties in the temperature �0.1 °C�, the elliptic tube surface areas �5%�, and

eating power �5%�, as well as those of geometrical parameters and consequences of their physicalarameters, uncertainties in thee average Nusselt number, friction factor, and Reynolds number arestimated as a maximum of 3.8%, 2.6%, and 3.2% respectively.

V. DATA REDUCTION

Using water on both sides of the heat exchanger can be performed with reasonable tempera-ure difference between hot and cold sides. The flow velocities and the Reynolds number arealculated from the measured flow rates based on the equivalent diameter. The tube equivalentiameter is calculated from the volume of water required to fill a given length of tubing. Deq isalculated in each case before turning on experiments by filling closed ended tested tube withwisted tape inserts by water. The volume of water is measured by putting this water in a mea-uring flask, which equals the volume of space �V� between the twisted tape and the elliptic tube,

Deq = �4V/�L�0.5. �1�

The tube cross-sectional flow area of the tube, At, is calculated by using tube equivalentiameter �At=�Deq

2 /4�. Reynolds number is calculated inside tubes as

Re = ��Deq/v� . �2�

he mean flow velocity inside the tube is given as

v = mc/��Deq2 l4� . �3�

he heat transfer rates of two fluid streams are calculated as

Qc = mcCpc�Tco − Tci� , �4�

Qh = mhCph�Thi − Tho� . �5�

he heat losses from the test section to the surrounding are calculated and maximum heat lossesre found to be about 2% from the total heat.

The average heat transfer coefficient for inside tube, hc, is calculated from the followingquation:

hc = Qc/��DeqL�tm� , �6�

here �tm is the logarithmic mean temperature difference, which is defined as

�tm = ��Tci − Tsi� − �Tco − Tso��/�ln�Tci − Tsi�/�Tco − Tso�� . �7�

he average Nu number is calculated based on the equivalent diameter as


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Nu = hcDeqlkc. �8�

he friction factor is calculated using the following equation:

f = �Deq/L��P/2�v2� , �9�

here �P is the pressure drop over length L.

. RESULTS AND DISCUSSION

. Results of average Nusselt number „Nu…

Preliminary experiments have been performed on a smooth circular tube to compare theesults with the empirical correlations that was proposed by Hewitt et al.21 to validate the presentesults. This correlation was stated as

Nu = 1.86�Re Pr D/L�0.33�a/�b0.14. �10�

The experimental Nu results of the present plain elliptic tube are compared with the presentlain circular tube and with Eq. �10� of the circular tube, as shown in Fig. 3. This figure representshe variation of the average Nusselt number �Nu� with Reynolds number for three cases. The Nuf the present experimental results of plain circular tube are found to agree within 5% with Eq.10� of the plain circular tube approximately, while the present Nu results of the plain elliptic tubere higher than that of both present and previous plain circular tubes.

Figures 4–8 show the relation of Nu with Re of the plain elliptic tube and an elliptic tube withnserted swirl sheet of different Y and S. These figures show that Nu increases with an increase ine, but it changes dramatically with Y and S. The same general shape of curves can be seen from

2

4

6

8

10

12

400 600 800 1000 1200 1400

Re

Nu

Present Circular tube

Present ellptic tube

Linear (Previous Work Ref.[21])

FIG. 3. Comparison between the present work and the previous work �Ref. 21�.

hese figures. The effect of Y on the Nu-S relation is shown in Fig. 8. These figures show that all


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u results of the elliptic tube with an inserted swirl sheet with different S and Y are greater thanhat of the plain elliptic tube. These figures show that Nu decreases with an increase in S and Y.he behavior of flow inside the elliptic tube with an inserted swirl sheet is affected by an increase

n S or Y. The increase in S or Y leads to a decrease in the turbulence intensity of the flow insidehe elliptic tube with an inserted swirl sheet and, in turn, a decrease in Nu. Thus, insertion of aelical screw sheet inside the tube makes swirls to flow and generates periodic disruptions to theevelopment of viscous boundary layer. This disturbance of main flow and viscous boundaryayers in a helical screw insert inside the tube enhances the heat transfer.

4

8

12

16

20

24

400 600 800 1000 1200 1400Re

Nu

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46

FIG. 4. Variation of Nu with Re of elliptic tube with different S at Y =0.22.

4

8

12

16

20

24

400 600 800 1000 1200 1400Re

Nu

No insertionS = 2.15S = 1.85S = 1.38S = 1S = 0.46

FIG. 5. Variation of Nu with Re of elliptic tube with different S and Y =0.27.


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. Results of friction factor „f…

Preliminary experiments have been performed on a smooth tube to compare the results withmpirical correlations that was proposed by Hewitt et al.21 to validate the present results. Thisorrelation is stated as

f = 64/Re. �11�

4

8

12

16

400 600 800 1000 1200 1400Re

Nu

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46

FIG. 6. Variation of Nu with Re of elliptic tube with different S at Y =0.31.

4

6

8

10

12

14

16

18

400 600 800 1000 1200 1400

Re

Nu

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46

FIG. 7. Variation of Nu with Re of elliptic tube without and with different inserted swirl sheets at Y =0.35.



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7

9

11

13

15

17

19

0 0.5 1 1.5 2 2.5

S

Nu

Y = 0.22

Y = 0.27

Y = 0.31

Y = 0.35

FIG. 8. Variation of Nu with S of elliptic tube at different Y and Re=1279.

0.03

0.05

0.07

0.09

0.11

0.13

0.15

400 550 700 850 1000 1150 1300

Re

f

Present circular tube

Present ellipticie tube

Linear (Previous circulartube Ref.[21])

FIG. 9. Comparison between the present work and the previous work �Ref. 21�.


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The experimental f results of the plain elliptic tube are compared with that of the plainircular tube and Eq. �11� of the circular tube, as shown in Fig. 9. This figure represents theariation of friction factor �f� with Reynolds number for three cases. The f of the present experi-ental results of the plain elliptic tube is slightly higher than that of the plain circular tube, while

he present results of the plain circular tube are found to agree within 7% with Eq. �11� of therevious plain circular tube.

The effect of Y and S on the characteristics of friction factor inside an elliptic tube with andithout an inserted swirl sheet will be discussed in the present section. The experiments have beenerformed at different Y and S to evaluate the direction of pressure drop. Figures 10–13 show theelation of f with Re for plain elliptic tube and elliptic tubes with inserted swirl sheets of different

and S. It is seen from these figures that the value of f decreases with an increase in Re, but itecreases with an increase in S. The same general shape of curves can be seen from all figures.he variation of f with S at different Y is shown in Fig. 14. This figure shows that the value of fecreases with an increase in Y. The behavior of flow inside an elliptic tube with an inserted swirlheet is affected by an increase in S or Y. The increase in S or Y leads to a decrease in theurbulence intensity of the flow inside the elliptic tube with an inserted swirl sheet and, in turn, aecrease in f .

. Correlation of the results

The experimental results are fitted, using power regression, to determine the following em-irical correlations for elliptic tubes:

Nu = 1.35 Re0.21 s−0.183Y−0.63 �12�

nd

f = 40.45 Re−0.92 s−0.131Y−0.229, �13�

here 5.86�102�Re�1.31�103 and 0.46�S�2.15 and 0.22�Y �0.35.The calculated data of Nucal and fcal from Eqs. �12� and �13� are plotted against the experi-

ental data of Nuexpt and fexpt in Figs. 15 and 16, respectively. As shown in these figures, theaximum deviation between experimental data and correlations are 8% and 10%, respec-

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

400 600 800 1000 1200 1400

Re

f

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46

FIG. 10. Variation of f with Re of elliptic tube at different S and Y =0.22.

ively.


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. Thermal performance

As shown in the present experimental results, there is an enhancement of the heat transferoefficient through elliptic tubes with an inserted swirl sheet, while an increment in frictionoefficient �f� occurs with a decrease in S and Y. The thermal performance factor �� is introducedo indicate the percentage increase in Nu over the percentage increase in f . To get optimumerformance between Nu and f for S and Y, the variations of thermal performance parameter ��

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

400 600 800 1000 1200 1400

Re

f

No insertionS = 2.15S = 1.85S = 1.38S = 1S = 0.46


0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

400 600 800 1000 1200 1400

Re

f

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46



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ith S and Y are shown in Figs. 17 and 18, respectively. These figures show that the maximumerformance parameter �� occurs at S=1 and Y =0.22. This means that for the present experi-ental results, the optimum operating values of S and Y are 1 and 0.22, which give an enhance-ent in the performance parameter of 19.7% and 42.3%, respectively.

0.04

0.06

0.08

0.1

0.12

0.14

0.16

400 600 800 1000 1200 1400

Re

f

No insertion

S = 2.15

S = 1.85

S = 1.38

S = 1

S = 0.46


0.05

0.06

0.07

0.08

0 0.5 1 1.5 2 2.5

S

f

Y = 0.22

Y = 0.27

Y = 0.31

Y = 0.35

FIG. 14. Variation of f with S of elliptic tube at different Y and Re=1279.


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I. CONCLUSION

Augmentation of laminar flow and heat transfer in elliptic tubes by means of helical screw-ape inserts is investigated experimentally. The friction factor in the horizontal double pipes oflliptic tubes with different parameters of S and Y is investigated. Cold and hot water are used asorking fluid in the tube side and shell side, respectively. The experiments covered a range ofeynolds numbers, 5.7�102�Re�1.31�103. The effects of S and Y on heat transfer augmen-

ation and friction factor have been presented.The results of the present investigation can be summarized as follows.

6

8

10

12

14

16

18

20

6 8 10 12 14 16 18 20

Nuexp

Nu

cal

+ 8 %

- 8 %

FIG. 15. Nucalc against Nuexpt for circular tube.

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

f exp

fcal

+ !" %

- !" %

FIG. 16. fcalc against fexpt for flat tube.



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0.8

0.9

1

1.1

1.2

1.3

1.4

0 0.5 1 1.5 2 2.5

S

η

FIG. 17. Variation of � with S at Y =0.31 and Re=1279.

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0 0.1 0.2 0.3 0.4 0.5

Y

η

FIG. 18. Variation of � with Y at S=1 and Re=1279.


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• The results indicate that the helical screw element of different Y and S have an effect on theresults of heat transfer coefficient and friction factor.

• The averaged Nusslet number �Nu� increases with an increase in the Reynolds number andwith a decrease in Y and S.

• The Nu of the plain elliptic tube is greater than that of the plain circular tube and the Nu ofelliptic tubes containing a helical screw tapes is better than that of the plain elliptic tubes forall Re, Y, and S.

• For a fixed Reynolds number, the friction factor �f� increases with a decrease in Y and S forthe elliptic tubes.

• The variation of thermal performance parameter �� with S and Y is presented. The �increases with an increase in S and Y until a point �S=1 and Y =0.22�, after that it graduallydecreases.

• The maximum performance parameter �� gives the optimum values of S=1 and Y =0.22.• The correlations of the average Nusselt number and friction factor with Re, S, and Y are

presented.

OMENCLATUREt Tube cross-sectional area �m2�p Specific heat capacity at constant pressure �J kg−1 K−1�

st Diameter of the twisted insertion �m�eq Equivalent diameter �m�

f Friction factor inside elliptic tubeLength of tube �m�Heat transfer coefficient �W m−2 k−1�Pitch between two turns of the twist sheet �m�Thermal conductivity �W m−1 k−1�

˙ Mass flow rate �kg s−1�u Average Nusselt numberP Pressure drop �N m−2�

Volume of water filling the tested tube �m3�Heat transfer �W�

e Reynolds numberPitch ratio �pitch/diameter of twist�, H /dst

Temperature �K�tm Logarithmic mean temperature difference

Velocity of water inside tube �m s−1�Width of twist sheet �m�Twist ratio �width of twist sheet/diameter of twist�, w /dst

reek lettersKinematics viscosity of water �m s−2�

a Viscosity of fluid at bulk temperature �kg m−1�b Viscosity of fluid at wall temperature �kg m−1�

Density of water �kg m−3�Thermal performance factor �Nu /Nu�� / �f / f��

ubscriptsColdHotInsideOutsideSurfaceWater
Plain tube

1

1

1

1

1

1

1

1

1

1

2

2


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1 S. Eiamsa and P. Promvonge, Sol. Energy 78, 483 �2005�.2 M. Yilmaz, O. Comakli, S. Yapici, and O. Sara, Energy Convers. Manage. 44, 283 �2003�.3 M. Yilmaz, O. Comakli, and S. Yapici, Energy Convers. Manage. 40, 1365 �1999�.4 W. J. Mamer and A. E. Bergles, J. Illum. Eng. Soc. 7, 11 �1978�.5 W. J. Mamer and A. E. Bergles, HTD �Am. Soc. Mech. Eng.� 43, 19 �1985�.6 W. J. Mamer and A. E. Bergles, Exp. Therm. Fluid Sci. 2, 252 �1989�.7 R. M. Manglik and A. E. Bergles, HTD �Am. Soc. Mech. Eng.� 68, 19 �1987�.8 R. M. Manglik and A. E. Bergles, J. Heat Transfer 115, 881 �1993�.9 R. M. Manglik and A. E. Bergles, J. Heat Transfer 115, 890 �1993�.0 M. A. Kedzierski and J. M. Goncalves, J. Enhanced Heat Transfer 6, 161 �1999�.1 S.-S. Hsieh, M.-H. Liu, and F.-Y. Wu, Int. J. Heat Mass Transfer 41, 1049 �1998�.2 S. Al-Fahed, W. L. Chamra, and W. Chakroun, Exp. Therm. Fluid Sci. 18, 323 �1998�.3 P. Sarma, T. Subramanyam, P. Kishorea, and S. Kakac, Int. J. Therm. Sci. 42, 821 �2003�.4 P. K. Sarma, P. S. Kishorea, V. D. Rao, and T. Subrahmanyam, Int. J. Therm. Sci. 44, 393 �2005�.5 S. Eiamsa-ard, C. Thianpong, and P. Promvonge, Int. Commun. Heat Mass Transfer 33, 1225 �2006�.6 P. Promvonge, Energy Convers. Manage. 49, 980 �2008�.7 S. W. Chang, Y. J. Jan, and J. S. Liou, Int. J. Therm. Sci. 46, 506 �2007�.8 P. Promvonge and S. Eiamsa-ard, Energy Convers. Manage. 47, 2867 �2006�.9 P. Promvonge and S. Eiamsa-ard, Int. Commun. Heat Mass Transfer 34, 849 �2007�.0 P. Promvonge and S. Eiamsa-ard, Exp. Therm. Fluid Sci. 32, 332 �2007�.1 G. F. Hewitt, G. L. Shires, and T. R. Bot, Process Heat Transfer �McGraw-Hill, London, 1994�.


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head transfer and friction factor inside elliptic tubes

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