Thermophoresis particle deposition: Natural convection interaction from vertical permeable surfaces embedded in a porous medium

This work deals with thermophoresis particle deposition on natural convection heat and mass transfer by steady laminar boundary layer flow over an isothermal vertical flat plate embedded in a fluid-saturated porous medium. The governing partial differential equations are transformed into nonsimilar form by using a special transformation, and then the resulting partial differential equations are solved numerically by using an implicit finite difference method. Different results are obtained and displaced graphically to explain the effect of various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the effect of increasing the porosity or thermophoresis wall coefficient is to increase the thermophoresis wall velocities, while the effect of increasing the dimensionless temperature ratio is to decrease the thermophoresis wall velocities for both cases of fluid suction or injection. Comparison with previously published work in the limits shows excellent agreement.