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RESEARCH PAPERS: Heat Conduction

On Hyperbolic Heat Conduction and the Second Law of Thermodynamics

[+] Author and Article Information
C. Bai

Department of Mechanical Engineering, Yeungnam University, Keungsan, Korea

A. S. Lavine

Mechanical, Aerospace, and Nuclear Engineering Department, University of California, Los Angeles, Los Angeles, CA 90095-1597

J. Heat Transfer 117(2), 256-263 (May 01, 1995) (8 pages) doi:10.1115/1.2822514 History: Received September 01, 1992; Revised May 01, 1994; Online December 05, 2007

Abstract

For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This scheme uses the characteristic properties of a hyperbolic equation and has no oscillation. By solving a model problem, we show that the conventional hyperbolic heat conduction equation can give physically wrong solutions (temperature less than absolute zero) under some conditions. The modified equation does not display these erroneous results. However, the difference between results of these two models is negligible except under extreme conditions.

Copyright © 1995 by The American Society of Mechanical Engineers
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