A numerical-analytical approach to the calculation of thermal fields with regard for the thermosensibility of the material of a medium and mixed boundary conditions

Abstract

We reasoned the efficiency of a combination of the indirect methods of boundary and near-boundary elements with the Kirchhoff transformation to construct a numerical-analytical solution of nonlinear three-dimensional heat conduction problems. We consider some dependence of thermophysical coefficients on the temperature and the intensity of internal sources. We built a discrete-continual model for problems with boundary conditions of the first, second, and third kinds using integral representations for the Kirchhoff transformation. The results of computation experiments are presented for the exponential and power-law dependences of the thermal conductivity on the temperature.