Abstract:Bearing elements of a number of strategic equipment are limited length rods with a variable cross-section. Most of them are exposed to certain types of heat sources. To ensure reliable operation of these equipment it is necessary to know the temperature field along the length of the rod with a variable cross section. This paper proposes a computational algorithm and method to determine the temperature field along the length of the rod with limited length and variable cross-section. They are based on fundamental laws of energy conservation. Also obtained is an approximate analytical solution of the problem.

In the work at the level of basic laws of conservation of energy combined with the use of quadratic spline functions a resolving system of equations is constructed. Herewith, the procedure is prepared to minimize the functionals of total thermal energy and potential energy of elastic deformation involving temperature field.

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In this article the computational algorithm and solution technique of the problem of identifying temperature field as well as strain and stress components throughout the rod length exposed to heat flows supplied to cross section areas of both ends and heat exchange in its lateral surface on the basis of heat quantity variation law are developed. Herewith the tested rod physical and mechanical properties are taken into account. The solutions so acquired are presented in a graphical form. Certain dependencies between temperature pivotal values and capacities of the set heat flows are found.

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