Simultaneous Identification of the Thermal Conductivity and Volumetric Heat Capacity of a Substance in the Three-Dimensional Case

The study of nonlinear problems related to the process of heat transfer in matter is of great practical importance. One of the problems arising in the study of the characteristics of new materials is the problem of simultaneous identification of the temperature-dependent thermal conductivity and volumetric heat capacity of a substance based on the results of experimental observations of the dynamics of the temperature field in an object. Previously, this problem was considered only in the one-dimensional case. Since experimental data are collected from three-dimensional objects, it is important that these studies be carried out for the three-dimensional case as well. In this paper, this problem is considered in the three-dimensional case. The consideration is carried out on the basis of the first boundary value problem for the three-dimensional non-stationary heat equation. The inverse problem of coefficient identification is reduced to a variational problem. The root-mean-square deviation of the calculated temperature field in the sample from its experimental value is chosen as the cost functional. Formulas for calculating the gradient of the cost functional are obtained. The results of the numerical solution of the formulated inverse problem are presented and discussed.

thermal conductivity, inverse coefficient problems, three-dimensional non-stationary heat equation, gradient