Heat transfer associated to natural convection flow in a partly porous cavity

The object of this study is the heat transfer associated to a buoyancy-induced flow developing in a rectangular cavity, partly filled with porous medium, with given heat flux from the sides. Numerical experiments show the existence of a quasi parallel solution away from the top and bottom end walls, characterized by a linear vertical temperature profile. Analytical expressions are derived for the velocity and temperature which, combined with an energy balance, enable us to relate the stratification to the other governing parameters. Influence of the porous layer's permeability and width, and of the Rayleigh number on the flow structure and heat transfer is thoroughly investigated, and summarized in simple relationships.