On Standard Eigenvalues of Variable-Coefficient Heat and Rod Equations

[+] Author and Article Information
H. P. W. Gottlieb

Division of Science and Technology, Griffith University, Nathan, Queensland, 4111 Australia

J. Appl. Mech 56(1), 146-148 (Mar 01, 1989) (3 pages) doi:10.1115/1.3176035 History: Received February 23, 1988; Revised June 09, 1988; Online July 21, 2009


Forms of the variable-heat-conductivity coefficient function in the one-dimensional heat equation are determined which yield a standard harmonic eigenvalue sequence as in the case of homogeneity. The continuous case is found to correspond to a four-thirds power law dependence on coordinate. For the stepped case, the condition on the ratio of segmental heat conductivities in terms of the junction location is presented.

Copyright © 1989 by ASME
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