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Flow field analysis through porous boundaries is of great importance, both in engineering and bio-physical fields, such as transpiration cooling, soil mechanics, food preservation, blood flow and artificial dialysis. A new family of exact solution of the Navier–Stokes equations for unsteady laminar flow inside rotating systems of porous walls is presented in this study. The analytical solution of the Navier–Stokes equations is based on the use of the Bessel functions of the first kind. To resolve these equations analytically, it is assumed that the effect of the body force by mass transfer phenomena is the ‘porosity’ of the porous boundary in which the fluid moves. In the present study the effect of porous boundaries on unsteady viscous flow is examined for two different cases. The first one examines the flow between two rotated porous cylinders and the second one discusses the swirl flow in a rotated porous pipe. The results obtained reveal the predominant features of the unsteady flows examined. The developed solutions are of general application and can be applied to any swirling flow in porous axisymmetric rotating geometries.

A new class of exact solutions of the Navier–Stokes equations for swirling flows in porous and rotating pipes