Temperature Profile in Semi-infinite Body With Exponential Source and Convective Boundary Condition

[+] Author and Article Information
B. F. Blackwell

Sandia National Laboratory, Aerothermodynamics Division 1553, Albuquerque, NM 87185

J. Heat Transfer 112(3), 567-571 (Aug 01, 1990) (5 pages) doi:10.1115/1.2910424 History: Received August 26, 1988; Revised July 15, 1989; Online May 23, 2008


An analytical solution for the temperature profile in a semi-infinite body with an exponentially decaying (with position) source and convective boundary condition is obtained using Laplace transforms. The appropriate dimensionless parameters are identified and the temperature as a function of these parameters is presented in graphic form. With cooling at the exposed surface, the maximum temperature occurs in the interior of the slab instead of at the exposed surface. The location of the temperature maximum as a function of the various system parameters is presented in graphic form. Approximate relationships are presented for small values of dimensionless time.

Copyright © 1990 by The American Society of Mechanical Engineers
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