The proposed work is devoted to the application of the direct method to the study of heat transfer processes in a multilayer flat structure. It is assumed that each layer is made of isotropic material of different thickness. There is an imperfect thermal contact between them, and the layers have internal heat sources. In this case, the isothermal surfaces are parallel planes, i.e the temperature changes in only one direction. On the outer surfaces of the structure there is a convective heat exchange with the environment, i.e the boundary conditions of the third kind are fulfilled. The coefficients of the thermal conductivity equation are considered to be piecewise constant with respect to the spatial coordinate. This is the first time the problem has been solved in this setting. The solution of the problem is realized by applying the method of reduction using the concept of quasi-derivatives and applying the theory of systems of differential equations with impulse action. The following is the procedure for separating Fourier variables using a modified method of eigenfunctions.Based on the physical content of the problem, the differential equation of thermal conductivity was written in the Cartesian coordinate system, but the solution scheme presented here without any fundamental difficulties extends to similar problems for multilayer bodies of basic geometric shapes by switching to appropriate coordinate systems. To illustrate the proposed method, a model example of finding the distribution of a nonstationary temperature field in a seven-layer flat structure under the influence of the hydrocarbon temperature of the fire is solved. The condition of ideal or non-ideal thermal contact is fulfilled between two adjacent layers. In addition, some layers have internal heat sources. The results of the calculations are presented in the form of a graph of temperature changes depending on timeand spatial coordinates.
Circulatory heat sources for canine respiratory heat exchange.
