Modelling and simulation of an industrial flow between two moving permeable surfaces

Fluid distribution within a channel formed by two permeable surfaces that are accelerated in the streamwise direction is controlled using the Navier-Stokes equations. The mathematical model of the problem is reduced to solving a single, fourth-order, nonlinear ordinary differential equation by numerical integration. The analytical solution is derived for low values of the Reynolds number. The numerical results enable to characterise the influences of the permeation Reynolds number and the surface accelerating parameter on the flow streamlines, pressure gradients, velocity distribution, and wall shear stresses. It is found that positive accelerating parameters cause the backward flow which gives the existence of collision zones inside the channel. Boundary layers take place by increasing the fluid injection Reynolds number at a fixed positive accelerating parameter, and by increasing the suction Reynolds number at a fixed negative accelerating parameter. These boundary layers stop the oscillations of normal pressure gradients in the flow field.