Analysis and solution of the ill-posed inverse heat conduction problem |
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Authors: | Charles F. Weber |
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Affiliation: | Oak Ridge National Laboratory, Computer Sciences Division, Post Office Box X, Oak Ridge, Tennessee 37830, U.S.A. |
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Abstract: | The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature and heat flux values on the surface. The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the one-dimensional case which replaces the heat conduction equation with an approximating hyperbolic equation. If viewed from a new perspective, where the roles of the spatial and time variables are interchanged, then an initial value problem for the damped wave equation is obtained. Since the formulation is well-posed, both analytic and numerical solution procedures are readily available. Sample calculations confirm that this approach produces consistent, reliable results for both linear and nonlinear problems. |
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