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Stationary temperature field in a rectangular plate with variable thermal conductivity in one coordinate

DOI: DOI: 10.17586/1606-4313-2023-22-1-99-104
UDC 536.2

Stationary temperature field in a rectangular plate with variable thermal conductivity in one coordinate

Kanareykin Aleksandr I.

For citation: Kanareykin A.I. Stationary temperature field in a rectangular plate with variable thermal conductivity in one coordinate. Journal of International Academy of Refrigeration. 2023. No 1. p. 99-104. DOI: 10.17586/1606-4313-2023-22-1-99-104

Abstract
The work is devoted to the issues of stationary heat transfer. The article presents a solution for the distribution of the temperature field in a rectangular plate, which leads to the fact that the problem is two-dimensional. In this case, the law of change of thermal conductivity along one of the coordinates is set. Therefore, the problem itself is asymmetric and nonlinear, which complicates the decision process itself. Heat exchange at the opposite ends of the plate surface occurs under boundary conditions of the third kind, there is no heat exchange at the other two ends. The solution was found by decomposition into a functional series. As a result, an analytical expression of the plate temperature distribution in the form of a Fourier series containing modified Bessel functions of the zero row is obtained. The paper also considered special cases when the boundary conditions on the walls are the same and when there is no heat supply. Special cases were interpreted physically. One of the special cases leads the problem to a problem with boundary conditions of the third kind, which indicates the reliability of the results obtained.

Keywords: rectangular plate, stationary thermal conductivity, two-dimensional differential equation of thermal conductivity, temperature, Fourier series, method of dividing variables, Bessel functions, boundary conditions of the third kind.

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