Non-Fourier Melting of a Semi-Infinite Solid

[+] Author and Article Information
M. H. Sadd, J. E. Didlake

Department of Mechanical Engineering, Mississippi State University, Mississippi State, Miss.

J. Heat Transfer 99(1), 25-28 (Feb 01, 1977) (4 pages) doi:10.1115/1.3450649 History: Received April 16, 1976; Online August 11, 2010


The melting of a semi-infinite solid subjected to a step change in temperature is solved according to a non-Fourier heat conduction law postulated by Cattaneo and Vernotte. Unlike the classical Fourier theory which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of a thermal disturbance is finite. The effect of this finite thermal wave speed on the melting phenomenon is determined. The problem is solved by following a similar method as used by Carslaw and Jaeger for the corresponding Fourier problem. Non-Fourier results differ from Fourier theory only for small values of time. Comparing the temperature profiles and the solid-liquid interface location for aluminum, differences between the two theories were significant only for times on the order of 10−9 –10−11 s and in a region within approximately 10−4 –10−5 cm from the boundary surface. However, these results are based on an approximate value of the thermal relaxation time.

Copyright © 1977 by ASME
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