Steady free convection flow with variable viscosity and thermal diffusivity along a vertical plate

Presents a study of the flow of a viscous incompressible fluid along a heated vertical plate, taking into account the variation of the viscosity and thermal diffusivity with temperature. The governing conservation equations of mass, momentum and energy are non-dimensionalized by using an appropriate transformation. The resulting system of coupled ordinary differential equations is solved analytically and numerically. Euler's transformation has been used to improve the analytical solution towards the numerical solution. The results show rather good agreement between the analytical and numerical solutions near the plate. It is found that the velocity f' of air or water near the plate increases as the viscosity decreases (the viscosity parameter alpha increases), but an opposite effect is noticed at a certain distance from the plate. It is observed that both the velocity and temperature of air increase as the thermal diffusivity of air increases (the thermal diffusivity parameter beta increases). For water it is found that the temperature theta decreases as the viscosity decreases ( alpha increases). The dimensionless shearing stress at the plate, the heat transfer rate at the plate, the momentum boundary layer thickness delta ₁, and the thermal boundary layer thickness delta ₂ are estimated for different values of alpha , beta and the Prandtl number sigma .