Hyperbolic Heat-Conduction Equation—A Solution for the Semi-Infinite Body Problem

[+] Author and Article Information
K. J. Baumeister

Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio

T. D. Hamill

McDonnell Douglas Astro. Corporation, Huntington Beach, Calif.

J. Heat Transfer 91(4), 543-548 (Nov 01, 1969) (6 pages) doi:10.1115/1.3580239 History: Received October 16, 1968; Online August 25, 2011


This theoretical paper determines the effect of the propagation velocity of heat on the temperature and heat-flux distribution in a semi-infinite body due to a step change in temperature at the surface. The solution yields a maximum but finite heat flux under the conditions of a step change. This is contrary to the infinite value predicted by the error function solution to the Fourier transient conduction equation. In addition, assuming convection is conduction limited, an upper limit for convective heat transfer coefficients is postulated.

Copyright © 1969 by ASME
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