Abstract
The article calculates the temperature field in an elliptical body with internal heat dissipation. In this case, the boundary conditions are boundary conditions of the third kind. The solution is located at the transition to the elliptic coordinate system. The author has obtained an analytical solution for the distribution of the temperature field in a body with an elliptical cross-section of infinite length with zero ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.
Highlights
The processes of heat transfer and associated mass transfer play an exceptional role in nature and technology
The main task of this paper is to find the distribution of the temperature field in a body with an elliptical cross-section of infinite length under boundary conditions of the third kind
The boundary condition of the third kind consists in setting a linear combination of the transport potential and its derivative with respect to the normal at the boundary of the considered region. Boundary conditions of this type play an important role in the theory of heat and mass transfer, since they are a mathematical formulation of the conditions of convective heat and mass transfer
Summary
The processes of heat transfer and associated mass transfer play an exceptional role in nature and technology. The flow of the working process in a variety of technological installations depends on them. In connection with the improvement of thermal equipment of energy-consuming and producing devices, a more accurate calculation of heat transfer processes in heat networks is required. A special place is occupied by bodies with an elliptical cross-section. Their peculiarity is that by manipulating the change in the length of the semi-axes of the ellipse, it is possible to obtain accurate analytical solutions to stationary problems of thermal conductivity for a very wide range of shape changes: from a cylinder to a thin plate. Several papers are devoted to the calculation of temperature fields in bodies of elliptical cross-section in the presence of internal heat sources under various conditions. This article is a continuation of the work [1]
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