Numerical simulation of the combined effects of thermophoretic motion and variable thermal conductivity on free convection heat transfer

In the current research, the effect of thermophoretic motion combined with temperature-dependent thermal conductivity on natural convection flow around the surface of a sphere at several circumferential locations has been presented. The modeled nonlinear governing partial differential has been transformed into a dimensionless form with the help of appropriate non-dimensional variables. Later, the finite difference method is applied to solve the proposed model. The effect of controlling parameters, such as thermal conductivity variation parameter γ, Prandtl number Pr, Schmidt number Sc, thermophoretic coefficient k, and thermophoresis parameter Nt on the velocity field, temperature distribution, mass concentration, skin friction, rate of heat transfer, and rate of mass transfer has been highlighted. The estimations of the emerging parameters on the physical properties are displayed in graphical and in tabular forms. It has been predicted that the rise in γ, Nt, Sc, Pr, and k increases the velocity distribution, but the reverse behavior has been seen in the temperature field. The enhancement in Nt, Sc, Pr, and k boosts up the curves of mass concentration, and the rise in γ suppresses the concentration function. It has been observed that an increase in γ reduces the skin friction and the rate of mass transfer but opposite behavior of the rate of heat transfer occurs. Furthermore, increasing values of Sc cause the skin friction to lose the dominance in the rate of heat and mass transfer. It has been also noticed that increasing values of Nt strengthen the skin friction and rate of heat transfer, and attenuation occurs in the case of the rate of mass transfer.