Transient and Steady Heat Conduction in Arbitrary Bodies with Arbitrary Boundary and Initial Conditions

[+] Author and Article Information
E. M. Sparrow

Universidade do Brasil, Rio de Janeiro, Brasil

A. Haji-Sheikh

Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, Texas

J. Heat Transfer 90(1), 103-108 (Feb 01, 1968) (6 pages) doi:10.1115/1.3597438 History: Received November 11, 1966; Online August 25, 2011


A method of analysis is described which yields closed-form solutions for two-dimensional heat conduction problems for bodies of arbitrary shape. Three-dimensional problems can also be treated without basic conceptual changes. The method accommodates rather general thermal boundary conditions including arbitrary spatial variations in surface temperature or in surface heat flux, or a convective (or linearized radiative) exchange with a fluid having spatially varying temperature and heat transfer coefficient. For transient problems, the initial temperature may be arbitrarily distributed. Once the solution method has been developed, its practical realization is rather direct, being facilitated by the use of widely available computer routines. A numerical example to illustrate the method is worked out.

Copyright © 1968 by ASME
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