Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations which pertaining to describe the continuity, momentum, energy and concentration. These equations involve the effects of viscous dissipation and chemical reaction . The numerical solutions of the dimensionless equations are found as a functions of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature (θ) and concentration (φ) as well as skin friction coefficient τ∗, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameters effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in thermophoretic parameter τ leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing couple stresses inverse parameter.