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RESEARCH PAPERS

Green’s Function Partitioning in Galerkin-Based Integral Solution of the Diffusion Equation

[+] Author and Article Information
A. Haji-Sheikh

Department of Mechanical Engineering, The University of Texas at Arlington, Arlington, TX 76019

J. V. Beck

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226

J. Heat Transfer 112(1), 28-34 (Feb 01, 1990) (7 pages) doi:10.1115/1.2910360 History: Received August 31, 1988; Online May 23, 2008

Abstract

A procedure to obtain accurate solutions for many transient conduction problems in complex geometries using a Galerkin-based integral (GBI) method is presented. The nonhomogeneous boundary conditions are accommodated by the Green’s function solution technique. A Green’s function obtained by the GBI method exhibits excellent large-time accuracy. It is shown that the time partitioning of the Green’s function yields accurate small-time and large-time solutions. In one example, a hollow cylinder with convective inner surface and prescribed heat flux at the outer surface is considered. Only a few terms for both large-time and small-time solutions are sufficient to produce results with excellent accuracy. The methodology used for homogeneous solids is modified for application to complex heterogeneous solids.

Copyright © 1990 by The American Society of Mechanical Engineers
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