, SIMULATION OF TEMPERATURE DISTRIBUTION WHEN HEATING A PLATE USING A MIXED HEAT CONDUCTIVITY EQUATION // BSU Bulletin. Mathematics, Informatics. - 2024. №1. . - С. 37-45.

SIMULATION OF TEMPERATURE DISTRIBUTION WHEN HEATING A PLATE USING A MIXED HEAT CONDUCTIVITY EQUATION

Работа выполнена при финансовой поддержке гранта РНФ № 23-21-00269, https://rscf.ru/project/23-21-00269/.

DOI: 10.18101/2304-5728-2024-1-37-45 UDK: 51-7, 517.95

The paper discusses a mathematical model and a finite- difference scheme for the heating process of a plate that is infinite in two spatial variables. The disadvantages of using the classical parabolic heat equation for this case and the rationale for using a mixed equation are given. Difference schemes use an integro-interpolation method to reduce errors. Two similar problems, but with different thermal conductivity co- efficients, were chosen as boundary value problems. In the first case, the thermal conductivity coefficient is linear, and in the second, it is nonlinear. To solve the equation with a nonlinear thermal conductivity coefficient, Newton’s method is used. The heat source in the parabolic part of the equation is equal to 0, and in the hyperbolic part of the equation sharp heating begins. The mixed problem with boundary conditions of the third kind is formulated and numerically solved.

hyperbolic heat equation, nonlinear equations, finite differ- ence method, third boundary condition, heat balance, hyperbolic-parabolic equations, Newton’s method.