Improved analytical solution for inverse heat conduction problems on thermally thick and semi-infinite solids

Analytical solutions to inverse heat conduction problems with a far-field boundary condition are derived for one- and two-dimensional problems using a Laplace transform technique. Accuracy of the predictions is improved by superposition of successive corrections to the function used to approximate the measured data. Long-term history of high frequency modes in both time and space is neglected noting that these components do not penetrate deeply into the solid. The two-dimensional solution is a relatively simple extension of the one-dimensional formulation. The present results are most useful for determining surface temperature and heat flux based on measured data from a row of sensors at a single depth below the surface and a known or measured boundary condition far from the surface.