Comparative Studies on Nonlinear Hyperbolic and Parabolic Heat Conduction for Various Boundary Conditions: Analytic and Numerical Solutions

[+] Author and Article Information
A. Kar, C. L. Chan, J. Mazumder

Laser Aided Materials Processing Laboratory, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Heat Transfer 114(1), 14-20 (Feb 01, 1992) (7 pages) doi:10.1115/1.2911240 History: Received November 16, 1990; Revised June 07, 1991; Online May 23, 2008


With the advent of lasers with very short pulse durations and their use in materials processing, the effect of thermal wave propagation velocity becomes important. Also, localized heating in laser-aided materials processing causes significant variations in the material properties. To account for these two effects, hyperbolic heat conduction is studied in this paper by considering all the thermophysical properties, except the thermal diffusivity, to be temperature dependent. The resulting nonlinear hyperbolic equations are linearized by using Kirchhoff transformation. Both analytical and numerical solutions are obtained for finite domains. Results are presented and compared with parabolic conduction results.

Copyright © 1992 by The American Society of Mechanical Engineers
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