The present work investigates the heat transfer characteristics of a laminar fully developed forced convection in a circular-sectored finned tube with axially uniform heat flux and peripherally uniform wall temperature. The tubes with circular-sectored fins are modeled as a fluid-saturated porous medium. Using the Brinkman-extended Darcy model for fluid flow and the two-equation model for heat transfer, the analytical solutions for both velocity and temperature distributions are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer in order to validate the porous medium approach. The agreement between the solutions based on the porous medium approach and the conventional method is close within 5.3 percent. Based on the analytical solutions, parameters of engineering importance are identified to be the angle of the circular sector α and the effective conductivity ratio C, and their effects on fluid flow and heat transfer are studied. Also, the total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of a tube with circular-sectored fins.

Issue Section:
Forced Convection
Keywords:
pipe flow, heat transfer, thermal resistance, optimisation, flow through porous media, temperature distribution, Forced Convection, Heat Transfer, Porous Media, Tubes
Topics:
Fins, Flow (Dynamics), Fluids, Heat transfer, Optimization, Porous materials, Temperature distribution, Thermal resistance, Fluid dynamics
1.
Bergles
,
A. E.
,
1997
, “
Heat Transfer Enhancement—the Encouragement and Accommodation of High Heat Fluxes
,”
ASME J. Heat Transfer
,
119
, pp.
8
–
19
.
2.
Webb, R. L., 1994, Principles of Enhanced Heat Transfer, John Wiley and Sons, New York, Chap. 8.
3.
Masliyah
,
J. M.
, and
Nandakumar
,
K.
,
1976
, “
Heat Transfer in Internally Finned Tubes
,”
ASME J. Heat Transfer
,
98
, pp.
257
–
261
.
4.
Watkinson, A. P., Miletti, D. L., and Kubanek, G. R., 1975, “Heat Transfer and Pressure Drop in Internally Finned Tubes in Laminar Oil Flow,” ASME Paper No. 75-HT-41.
5.
Rustum
,
I. M.
, and
Soliman
,
H. M.
,
1988
, “
Numerical Analysis of Laminar Forced Convection in the Entrance Region of Tubes with Longitudinal Internal Fins
,”
ASME J. Heat Transfer
,
100
, pp.
310
–
313
.
6.
Fabbri
,
G.
,
1998
, “
Heat Transfer Optimization in Internally Finned Tubes Under Laminar Flow Conditions
,”
Int. J. Heat Mass Transf.
,
41
, pp.
1243
–
1253
.
7.
Rustum
,
I. M.
, and
Soliman
,
H. M.
,
1988
, “
Experimental Investigation of Laminar Mixed Convection in Tubes with Longitudinal Internal Fins
,”
ASME J. Heat Transfer
,
110
, pp.
366
–
372
.
8.
Patankar
,
S. V.
,
Ivanovic
,
M.
, and
Sparrow
,
E. M.
,
1979
, “
Analysis of Turbulent Flow and Heat Transfer in Internally Finned Tubes and Annuli
,”
ASME J. Heat Transfer
,
101
, pp.
29
–
37
.
9.
Carnavos
,
T. C.
,
1980
, “
Heat Transfer Performance of Internally Finned Tubes in Turbulent Flow
,”
Heat Transfer Eng.
,
4
, pp.
32
–
37
.
10.
Webb
,
R. L.
, and
Scott
,
M. J.
,
1980
, “
A Parametric Analysis of the Performance of Internally Finned Tubes for Heat Exchanger Application
,”
ASME J. Heat Transfer
,
120
, pp.
38
–
43
.
11.
Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, London.
12.
Hu
,
M. H.
, and
Chang
,
Y. P.
,
1973
, “
Optimization of Finned Tubes for Heat Transfer in Laminar Flow
,”
ASME J. Heat Transfer
,
95
, pp.
332
–
338
.
13.
Soliman
,
H. M.
, and
Feingold
,
A.
,
1977
, “
Analysis of Fully Developed Laminar Flow in Longitudinal Internally Finned Tubes
,”
Chem. Eng. J.
,
14
, pp.
119
–
128
.
14.
Koh
,
J. C. Y.
, and
Colony
,
R.
,
1986
, “
Heat Transfer of Microstructures for Integrated Circuits
,”
Int. Commun. Heat Mass Transfer
,
13
, pp.
89
–
98
.
15.
Tien, C. L., and Kuo, S. M., 1987, “Analysis of Forced Convection in Microstructures for Electronic System Cooling,” Proc. Int. Symp. Cooling Technology for Electronic Equipment, Honolulu, Hawaii, 1987, pp. 217–226.
16.
Kim
,
S. J.
, and
Kim
,
D.
,
1999
, “
Forced Convection in Microstructures for Electronic Equipment Cooling
,”
ASME J. Heat Transfer
,
121
, pp.
639
–
645
.
17.
Kim
,
S. J.
, and
Kim
,
D.
,
2000
, “
On the Local Thermal Equilibrium in Microchannel Heat Sinks
,”
Int. J. Heat Mass Transf.
,
43
, pp.
1735
–
1748
.
18.
Srinivasan
,
V.
,
Vafai
,
K.
, and
Christensen
,
R. N.
,
1994
, “
Analysis of Heat Transfer and Fluid Flow Through a Spirally Fluted Tube Using a Porous Substrate Approach
,”
ASME J. Heat Transfer
,
116
, pp.
543
–
551
.
19.
Vafai
,
K.
, and
Tien
,
C. L.
,
1981
, “
Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media
,”
Int. J. Heat Mass Transf.
,
24
, pp.
195
–
203
.
20.
Slattery, V. C., 1999, Advanced Transport Phenomena, Cambridge University Press, Cambridge, pp. 194–197.
21.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp., New York.
22.
Sparrow
,
E. M.
, and
Haji-Sheikh
,
A.
,
1965
, “
Laminar Heat Transfer and Pressure Drop in Isosceles Triangular, Right Triangular and Circular Sector Ducts
,”
ASME J. Heat Transfer
,
87
, pp.
426
–
427
.
23.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd ed., Prentice Hall, New Jersey.
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