A function estimation approach for determining temperature-dependent thermophysical properties

The estimation of the temperature dependence of thermophysical properties has been generally treated as a parameter estimation problem in the literature. In this paper, we apply a function estimation approach to the inverse problem of determining the temperature dependence of either the volumetric heat capacity or the thermal conductivity. No information regarding the functional form of the unknown property is required in the present approach, and the minimization is performed in an infinite dimensional space of functions. The Conjugate Gradient Method with Adjoint Equation is used in the inverse analysis. Results obtained by using simulated temperature measurements of a single sensor, slow that the present approach is capable of recovering functions containing discontinuities, which are the most difficult to be recovered by an inverse analysis. The effects of sensor location on the inverse problem solution are also addressed on the paper.