A scale analysis of turbulent heat transfer driven by buoyancy in a porous layer with homogeneous heat sources

A heat transfer analysis is conducted for the turbulent natural convection in a porous layer with homogeneous heat sources. It is assumed that the top and the bottom of the layer is cooled at a constant temperature and insulated, respectively. Darcyʹs law is used to explain characteristics of fluid motion. Through a scale analysis on the turbulent heat and momentum transfer, a scale relation for Nusselt number is derived as a function of Rayleigh number. With the aid of available experimental and analytical results, Nusselt number correlations are proposed. The critical Rayleigh number for the onset of convection is also mentioned.