Melting effect on natural convection about axisymmetric stagnation point on a surface in porous media with soret and dufour effects and temperature Dependent viscosity

A three-dimensional boundary layer solution is presented for melting effect on heat and mass transfer by natural convection with temperature-dependent viscosity in the vicinity of an axisymmetric stagnation point on heated vertical surfaces in porous media in the presence of Soret and Dufour effects. The governing equations for the velocity, temperature and concentration fields are solved numerically by the fourth order Runge Kutta integration scheme. A parametric study illustrating the influence of the Darcy number, melting parameter or Stefan number, viscosity parameter, Dufour number and Soret number on the skin friction coefficient, Nusselt number as well as the Sherwood number are investigated. The results of the parametric study are shown in graphical and tabulated forms. It is found that increasing the Darcy number and the melting parameter within the boundary layer leads to increases in the velocity within the boundary layer and thus, increases the local skin friction coefficient. On the other hand, as the Darcy number and the melting parameter increase, the thermal boundary layer thickness decreases and thus, the rates of heat and mass transfer increase. As the Dufour number increases (or the Soret number decreases), the local skin friction coefficient increases and the local surface concentration decreases and thus increasing the local Sherwood number. Also, increasing the Dufour number tends to increase the local surface temperature and thus, decreasing the local Nusselt number.