Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions

Analytical solutions of Couette–Poiseuille flow of Bingham fluids between two porous parallel plates are derived. This study extends the work of Tsangaris et al. [S. Tsangaris, C. Nikas, G. Tsangaris, P. Neofytou, Couette flow of a Bingham plastic in a channel with equally porous parallel walls, J. Non-Newtonian Fluid Mech. 144 (2007) 42–48] to a general situation where the slip effect at the porous walls is considered. It is found that the form of the flow inside the channel depends not only on the Bingham number Bn, the Couette number Co (related to the moving wall) and the transverse Reynolds number Re, but also on the slip parameter Cs at the porous walls. In both the Co–Re diagram and the Co–Bn diagram, the region where plug flow appears enlarges as the slip effect increases, especially in the case where Co is negative. In the case where plug flow and double shear flow coexist, the transverse position of the plug flow and the shear rate at the boundaries exhibit two opposite behaviors when Cs increases, depending on the value of the other three dimensionless numbers. In other cases, slippage always weakens the shearing deformation of the flow.