Analytical and numerical solutions to a problem of convection in a porous media with lateral mass flux

We consider the problem of convection in a porous medium adjacent to a heated vertical porous plate. This problem has applications in the re-injection of hot water into a geothermal reservoir 1]. For large Rayleigh numbers, thermal boundary layers are formed and boundary layer theory is the obvious method of investigation. A similarity solution can be obtained when it is stipulated that the wall temperature and the lateral mass flux are power law functions of distance along the plate. In two particular cases, analytical solutions are found. In other cases, the profiles of the normalized velocity and temperature are obtained with accute accuracy using the “quasilinerization” method.