Temperature distribution in a body of elliptical cross-section without internal heat sources under boundary conditions of the third kind

Аuthors

Kanareykin A. I.

Sergo Ordzhonikidze Russian State University for Geological Prospecting, Moscow, 117997, Russia

e-mail: kanareykins@mail.ru

Abstract

The processes of heat transfer and the mass exchange resulting from it play today an important role in both technical sphere and nature. A formidable layer of works is devoted today to the heat exchange processes studying. Of particular scientific interest are the works describing modern heat exchange elements of heat exchange equipment with detailed description of their manufacturing methods, as well as the control of a heat exchanger with variable area of heat exchange surface. A new trend is being formed to date, which implies inclusion of material features and properties in the mathematical models being developed. Thus, functional dependencies are being increasingly included in the of heat and mass transfer processes modeling. It is known currently that a large surface for heat transfer is necessary for the best cooling of the elements. The surface can be enlarged by either finning or replacing the round bars, which have a minimum area, with other bars with an increased cross-section, such as oval or elliptical cross-section.

However, the temperature distribution in an elliptical body is not studied enough. This article deals with the problem of finding the temperature field in a body of elliptical cross-section without internal heat sources. The boundary conditions herewith are boundary conditions of the third kind. The article presents a solution for the temperature field distribution in a body with an elliptical cross-section at a given ambient temperature. The solution was obtained for the case in the system of elliptic coordinates. The obtained result is interesting since the temperature distribution does not depend on the boundary conditions, but is completely determined by the ambient temperature and the geometric size of the body.

Keywords:

heat transfer, temperature field, elliptic cross section, boundary conditions of the third kind, elliptic integral

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