Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid

A mathematical model is analyzed in order to study the heat and mass transfer characteristics in mixed convection boundary layer flow about a linearly stretching vertical surface in a porous medium filled with a viscoelastic fluid, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved analytically using the homotopy analysis method (HAM) to determine the convergent series expressions of velocity, temperature and concentration. The physical interpretation to these expressions is assigned through graphs and a table for the wall shear stress f ′ ′ ( 0 ) , Nusselt number - θ ′ ( 0 ) and Sherwood number - ϕ ′ ( 0 ) . Results showed that the fields were influenced appreciably by the effects of the governing parameters: mixed convection parameter λ , Lewis number Le, Prandtl number Pr, viscoelastic parameter K, concentration buoyancy parameter N, porosity parameter γ , Dufour number D f and Soret number Sr. It was evident that for some kind of mixtures such as the light and medium molecular weight, the Soret and Dufour’s effects should be considered as well.