Novel Similarity-Solution Which Is Applicable for Free Convection Over a Body of Arbitrary Shape: Thermal Non-Equilibrium in a Porous Medium

Abstract

-The study of the natural convection flow and heat transfer from hot surfaces in a porous medium has been of considerable interest in energy-related engineering problems. This paper is concerned with the free convection heat transfer over an arbitrary hot surface in a porous medium. It is assumed that the fluid and solid phases are not in local thermal equilibrium and therefore a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are used and transformed into ODE's. The similar equations obtained are solved numerically and the local heat flux is shown for three types of axisymmetric shapes, i.e., a vertical plate, horizontal cylinder and sphere. The results have also been validated with the available results in the literature; which show that our assumptions and numerical method are accurate. Mathematical derivation of a similarity solution for an arbitrary geometry in the heat transfer analysis is the main novelty of the present study.