Differentical equations, dynamical systems and optimal control

Correctness of a complex heat transfer model based on the simplified spherical harmonics method of the third order

G. V. Grenkin

Vladivostok State University, ul. Gogolya, 41, 690014, Vladivostok, Russia

Abstract: The paper deals with a system of equations that describes steady-state process of radiative-conductive heat transfer in a bounded domain with boundary conditions of specular and diffuse reflection of radiation and boundary conditions of the third kind for temperature. For the description of radiative energy field, the $SP_3$ approximation of the simplified spherical harmonics method is used. We establish properties of existence and uniqueness of the solution of the boundary value problem under constraints on coefficients in boundary conditions which are fulfilled over entire range of feasible physical data.

Keywords: radiative heat transfer, $SP_3$ approximation, $SP_N$ approximation, cross diffusion, unique solvability.

UDC: 517.95

MSC: 35R30

Received August 1, 2023, published May 28, 2024

DOI: 10.33048/semi.2024.21.025