THREE-DIMENSIONAL THERMAL CONDUCTIVITY PROBLEM FOR A MULTILAYER PLATE WITH IMPERFECT THERMAL CONTACT BETWEEN ITS LAYERS

Abstract

Purpose. It consists in obtaining an analytical expression for calculating the temperature at the points of a multilayer plate under the condition of imperfect thermal contact between its layers, presenting obtained formulas in a for convenient for numerical implementation and investigating the influence of the thermal resistance coefficient on the temperature distribution in the plate layers. Research methods. To solve the given problem, the method of integral transformations (double integral Fourier transform) and the method of compliance functions were used. Results. In the form of improper Fourier integrals the formulas for calculating the temperature at any point of the multilayer plate were obtained. Numerical results for three-layer plates were conducted, on the outer surfaces of which a thermal load that uniformly distributed over the square (the intensity of the thermal loads on the lower boundary is ten times more than on the upper one) was given. The graphs that illustrate the influence of the thermal resistance coefficients on the temperature distribution at the points of the lower boundaries of the first and second layers were obtained. It was shown that the raise of the coefficients of thermal resistance leads to decreasing of the temperature at the points of these boundaries. The proposed method can be used to determine the temperature at the points of the plates with any finite number of layers. Scientific novelty. For the first time, the three-dimensional problem of thermal conductivity for the layered plate with imperfect thermal contact between its layers was solved by the method of compliance functions. Previously, only two-dimensional and axisymmetric problems of this type were solved by this method. Practical value. The obtained results can be used as the test ones when performing analogous calculations by other methods. Based on the results of numerical calculations in designing layered structures, it is possible to select their elements with the necessary thermal characteristics.