Analysis and solution of the illposed inverse heat conduction problem
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 illposed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the onedimensional 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 wellposed, 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.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 November 1981
 DOI:
 10.1016/00179310(81)901447
 Bibcode:
 1981IJHMT..24.1783W
 Keywords:

 Conductive Heat Transfer;
 Heat Flux;
 Surface Temperature;
 Temperature Distribution;
 Approximation;
 Boundary Value Problems;
 Computer Programs;
 Hyperbolic Differential Equations;
 Numerical Stability;
 Fluid Mechanics and Heat Transfer