Convective fluid flow and heat transfer in a vertical rectangular duct containing a horizontal porous medium and fluid layer

Purpose The purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer. Design/methodology/approach The Darcy-Brinkman-Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions. Findings It is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained. Originality/value To the author's best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.