Abstract
The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.
Highlights
Various technological processes involve, as an important part, conductiveradiative heat transfer due the high temperatures characterizing the process
We mention only few of them: glass fabric production [3, 4]; glass melting and fining [8]; crystal growth in the production of semiconductors [10]
Analogous to (2.1) problems arise in conductive-radiative heat transfer, see, for instance, M
Summary
As an important part, conductiveradiative heat transfer due the high temperatures characterizing the process. The corresponding mathematical model for conductive-radiative steady-state heat transfer was suggested and investigated by M. The standard mathematical model for the steady-state conductive-radiative heat transfer in a system with simple geometry (see Fig. 1) according to [9] is. The aim of this paper is to give a theoretically strictly convergent iterative procedure for solving the problem (1.1).
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