Mathematical model of the third boundary value problem for mixed equation with variable thermal conductivity and nonlinear heat source

The study analyzes numerical solution of mathematical model of mixed nonlinear heat conduction equation with boundary conditions of the third type. The presented model reflects the procedure for eliminating arc discharge during short circuits in high-voltage electric networks, considering additional interval of stable arc combustion before the moment of circuit breakage and the replacement of hyperbolic heat conduction equation with hyperbolic-parabolic one. The article emphasizes equation replacement, since the phenomenon under consideration is characterized by a highly intensive dependence and for which the standard theories on the proportionality of flux density to potential gradient vector comes from phenomenological concepts and leads to infinite velocity of disturbance propagation, which contradicts immutable laws of physics. At the same time, the solution of the problem is carried out by numerical methods using implicit difference scheme using the finite volume method.