Couette–Poiseuille flow of a Bingham fluid through a channel overlying a porous layer

Abstract

Abstract Couette–Poiseuille flow of a Bingham fluid through a channel overlying a porous layer has been investigated in this study. Such flows are relevant in drilling muds for oil recovery, blood flow in biological systems, etc. An analytical solution of the velocity profile was derived from first principles. Effects of various parameters, like, Couette number (Co), Bingham number (Bn), Darcy number, slip coefficient, depth of porous layer on the velocity profile were studied in detail. The phase space plot of Couette–Bingham number was generated to obtain the region of double shear flow desirable for enhanced convective flow. Effects of other operating parameters on Co–Bn phase space were also investigated in order to identify a feasible region to operate for ensuring double shear flow. Locations of both yield surfaces due to asymmetric flow were obtained and effects of operating conditions on them were investigated. Variation of wall shear stress with operating conditions was also quantified. The present analysis will be beneficial for efficient design of flow channels dealing with viscoplastic fluids in real life applications.