Thermal Optimization of an Internally Finned Tube Using Analytical Solutions Based on a Porous Medium Approach

[+] Author and Article Information
Kyu Hyung Do, Jung Yim Min, Sung Jin Kim

Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea

J. Heat Transfer 129(10), 1408-1416 (Jan 30, 2007) (9 pages) doi:10.1115/1.2754866 History: Received May 08, 2006; Revised January 30, 2007

The present work deals with thermal optimization of an internally finned tube having axial straight fins with axially uniform heat flux and peripherally uniform temperature at the wall. The physical domain was divided into two regions: One is the central cylindrical region of the fluid extending to the tips of the fins and the other constituted the remainder of the tube area. The latter region including the fins was modeled as a fluid-saturated porous medium. The Brinkman-extended Darcy equation for fluid flow and two-equation model for heat transfer were used in the porous region, while the classical Navier–Stokes and energy equations were used in the central cylindrical region. The analytical solutions for the velocity and temperature profiles were in close agreement with the corresponding numerical solution as well as with existing theoretical and experimental data. Finally, optimum conditions, where the thermal performance of the internally finned tube is maximized, were determined using the developed analytical solutions.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematics of (a) an internally finned tube and (b) an equivalent porous medium

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Figure 2

Distributions along the interface between regions I and II: (a) interfacial velocity and (c) temperature profiles presented by Min and Kim (22), and (b) interfacial velocity and (d) temperature profiles used in the present study

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Figure 3

Comparison of the analytical solutions with the numerical solutions for (a) velocity and (b) temperature profiles (l=0.7, ε=0.6, N=10, ks∕kf=100)

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Figure 4

Comparison of the analytical solutions with the experimental data (5) for the friction factor

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Figure 5

Comparison of f Re between the theoretical results (14) and the present results for β=6deg

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Figure 6

Effect of the conductivity ratio on the averaged solid temperature profiles (l=0.7, ε=0.6, N=10)

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Figure 8

The variation of the optimized thermal resistances in terms of dimensionless fin height l under the condition of the fixed pumping power (Do=50mm, L=1m, P.P.=2.0×10−5W)

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Figure 9

The effects of (a) the pumping power and (b) tube diameter on the thermal performance of the internally finned tube

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Figure 7

Effect of the number of fins on the averaged solid temperature profiles (l=0.9, ε=0.6, and ks∕kf=100)



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