DIRECT METHOD OF STUDYING HEAT EXCHANGE IN MULTILAYERED BODIES OF BASIC GEOMETRIC FORMS WITH IMPERFECT HEAT CONTACT

Abstract

Purpose: The aim of the work is to study heat transfer processes in multilayer bodies of basic geometric shapes simultaneously under conditions of convective heat transfer on its surfaces and taking into account imperfect thermal contact between the layers. Method: To achieve this goal, a direct method was applied to solve a one-parameter family of boundary value problems in the theory of heat conduction. This method is based on the reduction method, the concept of quasiderivatives, a system of differential equations with impulse action, the method of separation of variables, and the modified method of eigenfunctions of Fourier. It is worth noting that the application of the concept of quasiderivatives allows you to circumvent the well-known problem of multiplication of generalized functions, which arises when using the differentiation procedure of the coefficients of a differential equation. Such a procedure, in our opinion, casts doubt on the equivalence of the transition to the differential equation obtained in this way with generalized coefficients. Results. The solution to the problem is obtained in a closed form. The proposed algorithm does not contain a solution to volume conjugation problems. It includes only: a) finding the roots of the corresponding characteristic equations; b) the multiplication of a finite number of known (2 × 2) matrices; c) the calculation of certain integrals; d) summing the required number of members of the series to obtain the specified accuracy. As an illustration, we consider model examples of heating eight-layer structures in a fire. Scientific novelty. For the first time, the direct method was applied to solving the problem of the distribution of an unsteady temperature field over the thickness of multilayer structures of basic geometric shapes simultaneously, in the presence of imperfect thermal contact between the layers. Practical significance. The implementation of the research results allows us to effectively study the heat transfer processes in multilayer structures, which are found in a number of applied problems.