Nonstationary thermal fields in inhomogeneous materials with nonlinear behavior of the components

We consider a two- or three-dimensional piecewise homogeneous body of any shape with temperaturedependent thermal characteristics. On the boundary of the body, we impose conditions of the first, second, and third kinds. The components of the body are in perfect thermal contact. We propose a procedure based on the joint application of the Kirchhoff transformation, the methods of near-boundary and boundary elements, and the stepwise time scheme of unique initial condition to the construction of the integral representations of temperature and heat flow at arbitrary space-and-time points. The numerical experiments reveal the efficiency of combining the indirect method of near-boundary elements with the Kirchhoff transformation in the case where the temperature dependence of the heat-conduction coefficient of the material is taken into account.