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Conduction

# Heat Conduction Through Eccentric Annuli: An Appraisal of Analytical, Semi-Analytical, and Approximate Techniques

[+] Author and Article Information
Manoj Kumar Moharana1 n2

Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal, Indiamkmoharana@gmail.com

Prasanta Kumar Das

Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal, Indiamkmoharana@gmail.com

1

Corresponding author.

2

Present address: A doctoral scholar at Department of Mechanial Engineering, Indian Institute of Technology Kanpur, Kanpur-208016 (U.P), India.

J. Heat Transfer 134(9), 091301 (Jun 29, 2012) (9 pages) doi:10.1115/1.4006391 History: Received March 27, 2011; Revised March 12, 2012; Published June 27, 2012; Online June 29, 2012

## Abstract

The problem of conduction heat transfer through an eccentric annulus with the inner surface kept at a constant temperature and the outer surface subjected to convective condition is solved by three different techniques. A perturbation analysis yields an analytical expression for temperature profile for small values of eccentricity. The two dimensional conduction problem has also been solved by a two dimensional semi-analytical technique in which the condition at the outer periphery is matched by a collocation technique. Finally, a one dimensional approximate technique namely sector method has been used to solve the same problem. The sector method does not require any numerical technique yet yields remarkable accuracy. Next, the heat flow through an eccentric insulation surrounding a circular cylinder was considered. It has been demonstrated that the sector method is effective also in determining the geometry of the critical insulation in this case over a wide range of radius ratio and Biot number. Finally, both all the three methods, i.e., the perturbation technique, the boundary collocation method and the sector method have been applied to determine the geometry of the critical as well as crossover perimeter of insulation around a circular cylinder when the insulation is provided eccentrically.

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## Figures

Figure 1

Geometrical details of an eccentric tube

Figure 2

(a) Symmetrical heat transfer module of the eccentric tube and (b) jth sector (counted in the anticlockwise direction) of the eccentric tube

Figure 3

Shape factor of the eccentric annulus with isothermal surfaces as function of e/ri and ro /ri

Figure 4

Variation of dimensionless heat transfer with Biot number at different geometry dimensions (i.e., e/ri and ro /ri )

Figure 5

Heat transfer ratio as a function of eccentricity; comparison of the predictions by the sector method and the perturbation technique with the boundary collocation method

Figure 6

Variation of heat dissipation with radius ratio in a concentric cylindrical system

Figure 7

Variation of heat dissipation with radius ratio in an eccentric system (a) e/ri  = 0.2 and (b) e/ri  = 0.4

Figure 8

Heat dissipation variation with radius ratio in an eccentric system (at different values of e/ri and Bi*)

## Errata

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