### 2005-01

by Qatanani, Naji A..

**Series:** 2005-01, Preprints

- MSC:
- 65M99 None of the above, but in this section
- 82C80 Numerical methods (Monte Carlo, series resummation, etc.)
- 45K05 Integro-partial differential equations

**Abstract:**

In this present paper we represent some important mathematical results on the physical model describing the heat transfer by conduction and radiation. The problem to be considered is the heat radiation exchange inside a non-convex body _ containing two conducting and opaque enclosures which are bounded by diffuse and grey surfaces and are surrounded by perfectly transparent and non-conductive medium. The combination of the radiation heat exchange with the normal heat conduction in _ yields a boundary value problem for the absolute temperature _ in stationary situation. Some properties of the heat radiative operator are represented and proved. The existence and the uniqueness of a weak solution of the non-local problem is also investigated.

**Keywords:**

heat transfer, heat conduction-radiation, Stefan-Boltzmann law, non-local boundary value problem, Integral operator, convex geometries