An inverse method for determining temperature-dependent thermophysical properties based on a remotely measured temperature history

An inverse methodology for determining an unknown boundary condition or temperature dependence of a thermophysical property was derived for a semi-infinite solid with temperature-dependent properties and time-varying, surface heating. Generalization was achieved by defining the boundary condition and thermal diffusivity (or conductivity) as simple polynomials, the unknown quantity with yet-to-be determined coefficients. To accomplish this, a measured thermal response determined away from the thermally loaded surface was fit to the generalized equation with unknown coefficients determined in a least-squares sense. Results including random and compounded errors added to the surface and remote data (up to ±5% each), along with inherent values in the thermal conductivity data, indicated that the method could be used to determine either a time-varying boundary condition or a thermal property. The proposed method is advantageous in that it can assess a wide temperature range, since the formulation is ultimately based on the surface temperature provided the thermal front had not reached the back boundary. Moreover, the least-squares smoothing inherent in the process may help minimize the influence of measurement errors.