Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity

Abstract

In this paper, we revisit a mathematical model representing a two-dimensional forced convection boundary-layer flow over a horizontal impermeable plate with a variable heat flux and viscosity. It is assumed that the fluid viscosity varies as an inverse linear function of temperature, the free stream velocity varies as an inverse linear of x and the wall heat flux varies with x as $x^{\lambda}$ ; where $\lambda > -1$ and x measures the distance along the surface. Analytical local similarity solutions are presented which reveal that there are two competing effects: $\lambda$ and $\theta_{e}$ ; where $\theta_{e}$ is the variable viscosity parameter. It has been shown that for $\theta_{e} > 0$ dual solutions exist and boundary separation occurs, while a unique local similarity solution exists for any $\theta_{e} < 0$ .