Authors

Heat exchange between cylindrical heating element and its shell under boundary conditions of the fourth kind

DOI: 10.17586/1606-4313-2023-22-3-68-73
UDC 536.2

Heat exchange between cylindrical heating element and its shell under boundary conditions of the fourth kind

Kanareykin Aleksandr I.

For citation: Kanareykin A.I. Heat exchange between cylindrical heating element and its shell under boundary conditions of the fourth kind. Journal of International Academy of Refrigeration. 2023. No 3. p. 68-73. DOI: 10.17586/1606-4313-2023-22-3-68-73

Abstract
The work is devoted to the issues of stationary heat transfer. In this article, the question of finding the temperature field of a heating element made in the form of a cylinder enclosed in a shell of the same cylindrical shape is considered. It is assumed that the thermal contact between the solid-coating system is ideal. In this case, heat exchange occurs under boundary conditions of the third and fourth kinds. In this paper, based on the methods of differentiation and integration, a solution was obtained to the problem of the distribution of the temperature field in both bodies. The resulting solution has an analytical form containing quadratic and logarithmic functions. Based on the obtained expression, a linear heat transfer coefficient and linear thermal resistance were found for this case. The reliability of the obtained result is confirmed by the fact that one of the special cases leads the problem to a problem with boundary conditions of the first kind, when the surface temperature is constant.

Keywords: heat exchange, temperature field, heating element, stationary thermal conductivity, cylinder, boundary conditions of the third kind, boundary conditions of the fourth kind, linear heat transfer coefficient, linear thermal resistance.

All references

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