An-Najah Staff

This article gives very signi…cant and up–to–date analytical results on the conductive– radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by di/use–gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.

In this paper a rigorous convergence and error analysis of the Galerkin boundary element method for the heat radiation integral equation in convex and non-convex enclosure geometries is presented. The convergence of the approximation is shown and quasi-optimal error estimates are presented. Numerical results have shown to be consistent with available theoretical results.

Our Main Concern In This Paper Is The Numerical Simulation Of The Heat Radiation Exchange In A Three-Dimensional Non-Convex Enclosure Geometry With A Diffuse And Grey Surface. This Physical Phenomena Is Governed By A Boundary Integral Equation Of The Second Kind. Due To The Non-Convexity Of The Enclosure The Presence Of The Shadow Zones Must Be Taken Into Account In The Heat Radiation Analysis. For That Purpose We Have Developed A Geometrical Algorithm To Provide An Efficient Detection Of These Shadow Zones That Are Needed To Calculate The Visibility Function. For The Discretization Of The Boundary Integral Equation We Have Used The Boundary Element Method Based On The Galerkin–Bubnov Scheme. The System Of Linear Equations Which Subsequently Arise Has Been Solved By The Conjugate Gradient Method With Preconditioning. To Demonstrate The High Efficiency Of This Method A Numerical Experiment Has Been Constructed For Non-Convex Geometry; The Heat Radiation In An Aperture Has Been Considered.

The radiation exchange in both convex and non-convex enclosures of diffuse gray surfaces is given in the form of a Fredholm boundary integral equation of the second kind. A boundary element method which is based on the Galerkin discretization schem is implemented for this integral equation. Four iterative methods are used to solve the linear system of equations resulted from the Galerkin discretization scheme. A comparison is drawn between these methods. Theoretical error estimates for the Galerkin method has shown to be in a good agreement with numerical experiments.

This article deals with the mathematical and the numerical aspects of the Fredholm integral equation of the second kind arising as a result of the heat energy exchange inside a convex and non-convex enclosure geometries. Some mathematical results concerning the integral operator are presented. The Banach fixed point theorem is used to guarantee the existence and the uniqueness of the solution of the integral equation. For the non-convex geometries the visibility function has to be taken into consideration, then a geometrical algorithm is developed to provide an efficient detection of the shadow zones. For the numerical simulation of the integral equation we use the boundary element method based on the Galerkin discretization scheme. Some iterative methods for the discrete radiosity equation are implemented. Several two- and three-dimensional numerical test cases for convex and non-convex geometries are included. This give concrete hints which iterative scheme might be more useful for such practical applications.

This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.

In this article we consider heat transfer in a non-convex system that consists of a union of finitely many opaque, conductive and bounded objects which have diffuse and grey surfaces and are surrounded by a perfectly transparent and non-conducting medium (such as vacuum). The resulting problem is non-linear and in general is non-coercive due to the non-locality of the boundary conditions. We discuss the solvability of the problem by proving the existence of a weak solution. We extend the analysis to address the parabolic case and to the case with non-linear material properties. Also we consider some cases when coercivity is obtained and state the corresponding stronger existence results.

In this article we focus our attention on the finite element error analysis for a problem involving both conductive and radiative heat transfer. We sketch the main steps of the analysis by stating the required a priori estimates and the final estimates. The proof for the estimate of the error due to approximation of the geometry is also presented. We prove an abstract estimate for the discretization error in a polygonal domain and combine it to the geometric estimate to yield the final error estimate. A concrete inverse monotone numerical method using view factors is analyzed using the abstract estimates.

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.