MATH35001 Viscous Fluid Flow: Flow through a porous channel with constant transverse velocity

Here's an illustration of the flow profile u(y) for the flow in a channel with porous walls. The flow is driven by an axial pressure gradient dp/dx = G. Fluid enters (and leaves) the channel through the porous walls which are located at y=0 and y=1 and the fluid has a constant transverse velocity v=-V. The flow profile is governed by the equation

For the animation below I have set rho=-G=mu=1. As the animation progresses, the transverse velocity V is increased from 0 to 50 (in equal steps). Note how this skews the initially symmetric (and parabolic) velocity profile. The pressure gradient G is kept constant and the increased viscous dissipation due to the large wall shear stress at the bottom wall (look at the velocity gradient at y=0!) reduces the overall flow rate through the channel as V increases.

Page last modified: October 26, 2007

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