Soluton Algorthim of Generalized Non-Stationary Heat Conduction Problem in the Bodies of Simple Geometric Shapes

The study proposes a single algorithm for solving the one-dimensional non-stationary heat conduction problems in the bodies of simple geometric shapes with internal energy sources of different nature. The bodies under consideration may have the shape of a plate, a rod (rib), a solid or hollow cylinder and a sphere. The basis of the problem solution is a generalized formulation of the heterogeneous differential equation of non-stationary heat conduction in partial derivatives for the bodies of the specified form and the method of integral transformations in finite bounds. The procedure for solving a specific boundary-value problem involves the presence of a mathematical model, but does not require integration of the differential equation of heat conduction. We give an example of determining the temperature field in a plate with unevenly distributed heat sources and different conditions of heat transfer at the boundary surfaces. It is relevant to use the solutions of this type, particularly, for testing the complex programs calculating the temperature field of thermal-loaded design elements, as well as for the analysis of the thermal regime in the early stages of design and substantiation of the eligible assumptions.

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