HOMOTOPY ANALYSIS OF SORET AND DUFOUR EFFECTS ON FREE CONVECTION NON-NEWTONIAN FLOW IN A POROUS MEDIUM WITH THERMAL RADIATION FLUX

This article analytically studies the combined laminar free convection flow with thermal radiation and mass transfer of non-Newtonian power-law fluids along a vertical plate within a porous medium. The mathematical model takes the diffusion-thermo (Dufour), thermaldiffusion (Soret), thermal radiation and power-law fluid index effects into consideration. The governing boundary-layer equations along with the boundary conditions are rendered into a dimensionless form by a similarity transformation. The powerful homotopy analysis method (HAM) is applied to obtain approximate analytical solutions for the resulting nonlinear differential equations. The effects of the radiation parameter (R), the power-law index (n), the Dufour number (Df), and the Soret number (Sr) on the velocity, temperature and species concentration fields are discussed in detail. The results indicate that when the buoyancy ratio of concentration to temperature is positive, N  0, the local Nusselt number increases with an increase in the power-law index and the Soret number or a decrease in the radiation parameter and the Dufour number. In addition, the local Sherwood number for different values of the controlling parameters is also obtained. The obtained solution, in comparison with the numerical solutions (fourth- order Runge–Kutta scheme) admit excellent accuracy.

Non-Newtonian fluid, Dufour number, Soret number, Nusselt number, Sherwood number, Homotopy analysis method, Similarity transformation, Chemical engineering