Combined Convection from a Vertical Flat Plate with Temperature Dependent Viscosity and Thermal Conductivity

We consider a two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity and thermal conductivity past a vertical impermeable flat plate. The equations governing the flow are transformed for three different regimes appropriate to the forced convection, free convection and forced-free convection regimes. The reduced equations for the forced convection and free convection regime are solved using the perturbation technique treating x the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained using the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. The effects of the viscosity variation parameter, e, and thermal conductivity parameter, g, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 1 to 100 are shown. The perturbation solutions obtained for small and large values of x are found in excellent agreement with the finite difference solutions for the entire x regime. We also present the values of the dimensionless velocity, viscosity and thermal conductivity showing the effects of viscosity and thermal conductivity parameter.