, NUMERICAL SOLUTION OF THE THIRD BOUNDARY VALUE PROBLEM FOR THE NONLINEAR MIXED HEAT CONDUCTION EQUATION // BSU Bulletin. Mathematics, Informatics. - 2023. №4. . - С. 14-21.

NUMERICAL SOLUTION OF THE THIRD BOUNDARY VALUE PROBLEM FOR THE NONLINEAR MIXED HEAT CONDUCTION EQUATION

DOI: 10.18101/2304-5728-2023-4-14-21 UDK: 519.63

The paper considers a mathematical model for a mixed non- linear heat equation with boundary conditions of the third kind. This MM models the process of switching off an electric arc in a co-current gas flow with the addition of a period of stable combustion until the alternating current crosses zero, when the arc is turned off. In this case, the strictly hy- perbolic heat equation obtained by the generalized Fourier law is replaced by a hyperbolic-parabolic one. The numerical calculation of the problem is carried out in two stages using an implicit conservative difference scheme, taking into account a variable thermal conductivity coefficient, a nonlinear heat source and a lateral heat sink. At the first quasi-stationary stage, a parabolic equation is considered, in which the thermal relaxation coeffi- cient is equal to zero. Its solution is used to formulate an initial boundary value problem for a hyperbolic equation at the moment the arc is turned off, where the specified coefficient becomes a constant value greater than zero. This second stage implements a significantly non-stationary process of turning off the electric arc.

hyperbolic heat equation, nonlinear mixed type equations, finite difference method, third boundary condition, heat balance.