Lie point symmetries for biological magneto-Jeffrey fluid flow in expanding or contracting permeable walls: a blood vessel model

Abstract

ABSTRACTThis article addresses biological flow in expanding or contracting blood vessels. The alternate contraction and expansion of vessels is known to act as a physiological pump to generate flow. When muscles compress blood vessel walls, the valve at the end of the source is closed, and the downstream end opens; for this reason, blood is pumped in the downstream direction. To study this situation, a model has been developed here that consists of the unsteady two-dimensional flow of an incompressible magneto-Jeffrey fluid in a porous semi-infinite channel with expanding or contracting walls; the channel is closed from one end by a compliant membrane. The Lie group analysis method was used to transform a system of nonlinear partial differential equations into nonlinear ordinary differential equations that were solved using the perturbation method. The effects of Jeffrey parameters (, which is the ratio of relaxation time to retardation time, and Deborah parameter ) and other physical parameters are plotted and discussed. We find that the axial velocity of a Newtonian fluid is greater than that of a non-Newtonian fluid if the walls are in contraction and vice versa if the walls are in expansion. If the walls are expanded, the blood is distributed in a large area, and thus, the normal pressure decreases, while if the walls are contracted, blood is distributed in less space, and thus, the pressure increases. Normal pressure in expanding blood vessels is less than that in contracting blood vessels.