A macroscopic model for the heat transfer in the chessboard-type nonhomogeneous media

The aim of this paper is to formulate, discuss and apply a certain macroscopic model of the heat transfer in the rigid chessboard-type micro-inhomogeneous conductor. To this end the tolerance averaging approach is applied. Within the framework of this approach a certain approximate solution to the periodic cell problem is proposed. It leads to the initial-boundary value problem for the averaged temperature field coupled with the initial value problem for the so-called internal variable vector field. In contrast to homogenization, the obtained model describes the effect of microstructure size on the overall behaviour of the medium. It is shown that the proposed model has a physical sense provided that the inhomogeneity of the medium is not too large.