Steady mixed convection boundary-layer flow over a vertical flat surface in a porous medium filled with water at 4°C: variable surface heat flux

The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water at 4°C (maximum density) when the surface heat flux varies as xm and the velocity outside the boundary layer varies as x(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions when the mixed convection parameter λ is greater than some critical value λc (dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λc is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and the limits as m → ∞ and as m → −1.