New numerical treatment of source term in convective transfer of heat between fluid and porous solid matrix

The purpose of this paper is to report a novel formulation of convective heat transfer source term for the case of flow through porous medium.

The novel formulation is obtained by analytical solution of an idealized dual problem. Computations are performed by dedicated tool for fixed bed combustion named GRATECAL and developed by the authors. However, the proposed method can also be applied to other porous media flow problems.

The new source term formulation is unconditionally stable and it respects exponential decay of temperature difference between the fluid and porous solid medium.

The results of this work are applicable in the simulation of convective heat transfer between the fluid and porous medium. Applications include e.g. fixed bed combustion, catalytic reactors and lime kilns.

The reported solution is believed to be original. It will be useful to all involved in numerical simulations of fluid flow in porous media with convective heat transfer.