Numerical simulation of the heat conduction in composite materials

Abstract

In this paper we develop and validate mathematical models and numerical algorithms for the heat transfer simulation in composite materials. The main features of the problem deal with the dependence of the heat source on the solution, discontinuous diffusion coefficients and nonlinear convection and radiation boundary conditions. The differential problem is approximated by the finite volume discrete scheme. It is proved that for a sufficiently small parameter, which defines the dependence of the source term on the solution, the discrete problem has a unique solution which converges to the solution of the differential problem. Linearization of the nonlinear problem is done by using the Picard method and the convergence of the iterations is proved. Results of numerical experiments are presented.

Keywords:

• heat conduction
• nonlinear boundary conditions
• finite volume method
• convergence analysis
• Picard's iterations