Modeling of the heat conduction process in composite media

In this work we proposed a two-channel model of heat conduction processes in composite media on the basis of the general transfer theory. The obtained system of equations can be reduced to both the generalized Fourier equation and the system of Cattaneo equations describing fast processes. The stability of the processes is considered. A system of equations for perturbations is obtained. The calculation of the perturbations’ spectrum is given depending on the parameters of the model. From this fact it follows that in a linear system the stationary process of heat conduction is stable with respect to any small perturbations. If we take into account nonlinearity even in the simplest cases it leads to the appearance of various instabilities and the excitation of heat waves.