Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

Abstract

Abstract. In this paper the velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium are obtained for the governing equations (Kaviany [7]) following the technique adopted by Chandrashekara [2] which are concerned with the interesting situations of the existence of transverse, velocity and thermal boundary layers. Here the pressure gradient is just balanced by the first and second order solid matrix resistances for small permeability and observed that by increasing of the flow resistance the asymptotic value for the heat transfer rate increases. Further we concluded that the transverse boundary layers are thicker than that of axial boundary layers. Hence we evaluated the expressions for the boundary layer thickness, the shear stress at the semi-infinite plate and ~r (the ratio of the thicknesses of the thermal boundary layer and momentum boundary layer). The variations of these quantities for different values of the porous parameter B and the flow resistance F have been discussed in detail with the help of tables. The curves for velocity and temperature distributions have been plotted for different values of B and E Lastly we have evaluated the heat flux q (x) and found that it depends entirely upon the Reynolds number Re, Prandtl number Pr,B and E In the limiting case B ~ 0, q (x) coincides with the well known Pohlhausen Formula.