Analysis of free surface momentum and energy transport in porous media

The phenomenological analysis of free surface transport through porous media is presented. A finite difference scheme using the Marker and Cell (MAC) method is employed to investigate the momentum and energy transport in a porous channel involving free surface transport phenomena. To the best of the authors' knowledge, this is the first investigation of free surface momentum and energy transport through porous media and is also the first application of the MAC method for exploring the free surface transport phenomena in a porous medium. Limiting case comparisons are made with an existing analytical solution for flow through a channel filled with a porous medium. Excellent agreement is obtained for both the temperature and velocity distributions. Temporal free surface positions are also compared and verified against an existing analytical solution. A detailed analysis of the encroachment of two immiscible fluids in a porous channel using Darcy's model is presented. The effects of pressure differences and permeabilities on free surface transport through a porous medium are investigated. The effect of the free surface transport in porous media on the energy transfer is also explored.