Thermal Field of a Cylindrical Body During Cyclic Heating

The article discusses the heating process of a cylindrical body under the cycling heat exposure onto its end surfaces. The mathematical model of the analyzed process includes a nonlinear differential equation of the parabolic type which considers a correlation between thermophysical properties of the matter and the temperature as well as the boundary conditions describing heat exchanges on the body surface. The article presents an algorithm of the non-stationary thermal field calculation based on the discretization of the differential equation with a small variable time step. At the k-th time step a temperature distribution within the cylindrical body is calculated by the double trigonometric Fourier series. Its coefficients are estimated by solving an infinite set of linear algebraic equations with the help of the reduction method. The authors give a numerical sample of calculating the non-stationary temperature field in the cylindrical body at the rate of cyclic impulse heating of its end surfaces. The dependence of different internal points of the cylindrical body on temperatures is tested.

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