Laminar Flow with Slip in Channels with Uniformly Porous Walls

The assumption of no slip does not accurately characterize momentum transfer near permeable walls. The influence of nonzero slip velocities on velocity profiles, pressure distribution, and friction coefficient are reported for laminar flow in a parallel plate channel with uniform suction or injection through its porous boundaries. The 2‐D Navier‐Stokes equations are reduced to a third‐order, nonlinear, ordinary differential equation with one free parameter by introducing an appropriate stream function that is then solved numerically. This solution is valid for arbitrary values of the wall Reynolds number $R_w$, based on the half‐channel height and the suction wall velocity. Suction at the porous boundary appears to have a greater impact on fluid mechanics compared to injection. It is observed that at a fixed value of the slip coefficient, increasing suction results in thinner momentum boundary layers whereas for a fixed wall Reynolds number, velocity profiles approach plug flow with increasing slip. It is also observed that the axial pressure drop decreases with the wall Reynolds number and even changes sign at $R_w\sim 1.31\text{.}$