An integral treatment for heat and mass transfer along a vertical wall by natural convection in a porous media

Abstract

This paper deals with the free convective heat and mass transfer along a vertical wall embedded in a fluid saturated porous medium by using an integral method of the Von-Karman type in the presence of temperature and concentration gradients. Mathematical expressions for the local Nusselt number and local Sherwood number have been derived in terms of boundary layer thickness ratio. The governing parameters for the flow-field are buoyancy ratio (N) and Lewis number (Le). The numerical values of the local Nusselt number and local Sherwood number have been computed for a wide range of values of N and Le. The variations of local Nusselt number and local Sherwood number with N have also been studied with the help of graphs for the different values of Le. Similarly, the variations of local Nusselt number and local Sherwood number with Le have been studied for different values of N with the help of graphs. It has been found that the local Nusselt number increases as N increases for the decreasing value of Le, whereas the local Sherwood number increases as N increases for the increasing values of Le. The local Nusselt number and the local Sherwood number increase as Le increases for increasing values of N. The numerical values of the thermal boundary layer and concentration boundary layer thicknesses have also been computed for the flow-field. It has been found that the results obtained by the integral method are in good agreement with those obtained by Bejan and Khair [Heat and Mass Transfer by Natural Convection in a Porous medium, Int. J. Heat Mass Transfer, 28, pp. 909-918, 1985].