Abstract
Laminar flows of two immiscible, incompressible fluids past permeable channels have been studied for the three cases of plane Couette flow, generalized Couette flow, and Poiseuille flow. The free-flow channel has two layers of immiscible fluids, while the porous region has been divided into a Brinkman layer and a Darcy layer. The Beavers−Joseph condition has been used to match velocities at the Brinkman−Darcy interface, while the continuity of velocities and stresses have been used at the interface of the free-fluid and Brinkman regions. Momentum and energy equations are solved analytically, yielding corresponding velocity and temperature profiles. Nusselt numbers are calculated for variations in viscosity ratios and Darcy numbers. We observe that modifications in these parameters lead to variations in Nusselt numbers and alterations in velocity and temperature profiles.
Published Version
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