6 research outputs found
On Existence and Uniqueness Theorem Concerning Time–Dependent Heat Transfer Model
In this article we consider a physical model describing time-dependent heat transfer by conduction and radiation. This model contains two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-grey surfaces. The aim of this work is to present a reliable framework to prove the existence and the uniqueness of a weak solution for this problem. The existence of the solution can be proved by solving an auxiliary problem by the Galerkin-based approximation method and Moser-type arguments which implies the existence of solution to the original problem. The uniqueness of the solution will be proved by using the same approach in our previous work for the stationary heat transfer model and some ideas from nonlinear heat conduction analysis
Use of the multigrid methods for heat radiation problem
We consider the integral equation arising as a result of heat
radiation exchange in both convex and nonconvex enclosures of
diffuse grey surfaces. For nonconvex geometries, the visibility
function must be taken into consideration. Therefore, a
geometrical algorithm has been developed to provide an efficient
detection of the shadow zones. For the numerical realization of
the Fredholm integral equation, a boundary element method based on
Galerkin-Bubnov discretization scheme is implemented.
Consequently, multigrid iteration methods, which are closely
related to two-grid methods, are used to solve the system of
linear equations. To demonstrate the high efficiency of these
iterations, we construct some numerical experiments for different
enclosure geometries