Nonsimilar combined convection flow over a vertical surface embedded in a variable porosity medium

The problem of combined forced-free convection flow over an isothermal vertical surface embedded in a variable porosity porous medium with heat generation or absorption is formulated. The formulation includes the porous medium inertia and boundary effects, variable porosity, and thermal dispersion. The developed governing equations are transformed into nonsimilarity equations that have the advantage of producing their solution at the leading edge of the surface. These equations are then solved numerically subject to appropriate boundary and matching conditions by an implicit, finite-difference method. Comparisons with previously reported numerical and experimental work on the special case where no porous medium is present are performed and found to be in excellent agreement. A parametric study of the physical parameters involved in the problem such as the particle diameter-based Reynolds number the Grashof number; the flow-based Reynolds number; and the heat generation or absorption coefficient is conducted. The obtained results are illustrated graphically to show interesting features of the solution. It is found that flow separation exists for the case of opposing flow condition and that the presence of thermal dispersion is essential for this type of problem.