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An exact solution of the Navier-Stokes equations for laminar flow inside porous pipes simulating variable suction and injection of blood flows is proposed in the present article. To solve these equations analytically, it is assumed that the effect of the body force by mass transfer phenomena is the ‘porosity’ of the porous pipe in which the fluid moves. The resultant of the forces in the pores can be expressed as filtration resistance. The developed solutions are of general application and can be applied to any swirling flow in porous pipes. The effect of porous boundaries on steady laminar flow as well as on species concentration profiles has been considered for several different shapes and systems. In certain physical and physiological processes filtration and mass transfer occurs as a fluid flows through a permeable tube. The velocity and pressure fields in these situations differ from simple Poiseuille flow in an impermeable tube since the fluid in contact with the wall has a normal velocity component. In the new flow model, a variation of the solutions with Bessel functions based on Terrill’s theoretical flow model is adopted.

An exact solution of the Navier-Stokes equations for swirl flow models through porous pipes