A Brief Compendium of Correlations and Analytical Formulae for the Thermal Field Generated by a Heat Source Embedded in a Porous Medium

This work reviews and compares suitable models for the thermal analysis of forced convection over a heat source in a porous medium. The set of available models refers to an infinite medium in which a fluid moves over different two heat source geometries: i.e. the moving infinite line source and the moving finite line source. In this perspective, the present work presents a plain and handy compendium of the above-mentioned models for forced external convection in porous media; besides, we propose a dimensionless analysis to figure out the reciprocal deviation among available models, helping the selection of the most suitable one in the specific case of interest. Indeed, the two solutions result practically equivalent to each other at given ranges of fluid velocity, length and time scales. Similarly, under specific conditions, the advection term becomes ineffective in terms of heat transfer performances, allowing the use of purely-conductive models. Therefore, one can choose the simplest solution, with significant benefits in terms of computational effort and interpretation of the results. The main outcomes presented in the paper are: the conditions under which the system can be considered subject to a Darcy flow, the minimal distance beyond which the finite dimension of the heat source does not affect the thermal field, and the critical fluid velocity needed to have a significant contribution of the advection term in the overall heat transfer process.