Research Papers: Conduction

Thermal Resistance Approach: An Engineering Tool for Improvement of Conductive Constructal Configurations

[+] Author and Article Information
M. Eslami

School of Mechanical Engineering,
Shiraz University,
Shiraz 71936-16548, Iran
e-mail: meslami@shirazu.ac.ir

K. Jafarpur

School of Mechanical Engineering,
Shiraz University,
Shiraz 71936-16548, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 28, 2013; final manuscript received April 9, 2014; published online May 9, 2014. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 136(8), 081301 (May 09, 2014) (10 pages) Paper No: HT-13-1602; doi: 10.1115/1.4027459 History: Received November 28, 2013; Revised April 09, 2014

In the last decade, various conductive networks for cooling heat generating bodies have been proposed, analyzed, and optimized. Nevertheless, many of these studies have not been based on an analytical or mathematical formulation of the effective parameters. In this trend, a new geometry is assumed and analyzed (by analytical or numerical methods) hoping to decrease the total thermal resistance of the system. Therefore, the objective of the present paper is to illustrate how to analyze a conductive cooling network and improve it using the analytical procedures based on the general formulation of thermal resistance. As an example, the conventional rectangular elemental volumes with I shaped conductive link is modified to V shaped and pencil shaped designs and optimized analytically. Moreover, general expressions for optimum local thickness and thermal resistance of the links with variable cross section in an arbitrary network are provided. It is shown that improvements up to 50% can be achieved easily by simple geometrical changes if the designer is equipped with a profound knowledge of the important governing parameters.

Copyright © 2014 by ASME
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Fig. 1

An I shaped rectangular elemental volume

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Fig. 2

A rectangular element with V shaped conductive links

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Fig. 3

A rectangular element with Y shaped conductive links

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Fig. 4

A first order construct with V shaped elements

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Fig. 5

A rectangular element with pencil shaped conductive links

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Fig. 6

Equation (27) has a flat minimum near x/L≈0.8

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Fig. 7

A pencil shaped tree with x/L = 0.5 and two probable points with maximum temperature

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Fig. 8

The optimum distribution of an infinite number of infinitesimal links

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Fig. 9

A general arbitrary link with variable cross section

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Fig. 10

A general network with links of variable and constant thickness

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Fig. 12

A pencil shaped network with variable cross section

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Fig. 11

A V shaped tree with optimum local thickness

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Fig. 13

(a) The present pencil shaped design developed analytically; (b) optimization results of Xu et al. [19] for a fixed rectangle by simulated annealing algorithm




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