Forced Convection Over a Backward-Facing Step with a Porous Floor Segment

Abstract

Forced convection after a backward-facing step, with a porous floor segment, is investigated numerically using the SIMPEC method. The Brinkman-Forcheimmer extended model is used to govern the flow in the porous-medium region. At the interface, the flow boundary condition imposed is a shear stress jump, which includes the inertial effect, together with a continuity of normal stress. The thermal interfacial condition is continuities of temperature and heat flux.

Results are presented for Reynolds number up to 800 and Darcy number up to 10⁻¹. Also varied are the length and depth of the porous segment. Compared with the case with no porous floor, the local heat transfer is augmented after the porous floor. Within the porous floor, the heat transfer is reduced, but this may be offset by using a porous medium of higher conductivity than the fluid. To obtain good heat enhancement after the porous segment, it should approximately match the length of the recirculation region. The porous segment should have large permeability (Darcy number around 10⁻¹), but it is not necessary that it be of great depth. The interfacial stress jump coefficients β and β ₁ are varied from − 5 to + 5, and some effects are observed on the local Nusselt numbers, velocity profile, and temperature distribution.