An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications

[+] Author and Article Information
O. R. Burggraf

Research Laboratories, Lockheed Missiles & Space Company, Palo Alto, Calif.

J. Heat Transfer 86(3), 373-380 (Aug 01, 1964) (8 pages) doi:10.1115/1.3688700 History: Received October 10, 1962


An inverse problem in unsteady heat conduction is one for which boundary conditions are prescribed internally, the surface conditions being unknown. By specifying the boundary conditions at a single location, an exact solution is obtained as a rapidly convergent series with the well-known, lumped capacitance approximation as the leading term. Specific forms of the series are determined for sample inverse problems: solid slab, cylinder, sphere, and transpiration-cooled slab. The solution also is applied to direct problems, involving two-point boundary conditions. By truncating the series, approximate solutions of simple form result. The one-term and two-term approximations compare well with exact solutions.

Copyright © 1964 by ASME
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