THE DETERMINATION OF THE UNKNOWN THERMAL PROPERTIES OF HOMOGENEOUS HEAT CONDUCTORS

Abstract

The aim of this paper is to determine the two constant parameters corresponding to the physical properties of a homogeneous heat conductor, namely, the heat capacity and the thermal conductivity, from heat flux and temperature measurements. An iterative nonlinear least-squares boundary element method is proposed. The inversion is performed for both exact and noisy measurements. Numerically, it is shown that the thermal properties can uniquely and stably be retrieved from two measurements containing at least one heat flux measurement for finite homogeneous heat conductors, whilst theoretically, for the semi-infinite conductor it is shown that one heat flux and one internal temperature measurement are necessary and sufficient.