Effect of Wall Properties Without/with Magnetic Field on NanoBingham Fluid Flows

Abstract

In this study the steady flow of nano Bingham plastic fluid with wall properties under the effect of an external magnetic field and the peristaltic motion has been analyzed. Flow of nano Bingham plastic fluid is considered as non-Newtonian fluid. The nanofluid interaction theory is investigated by considering equations of motion of both the nanofluid and flexible boundary. The governing equations are solved analytically under the long wavelength and low Reynolds number approximation. Analytical forms estimates are obtained for the velocity profile, volumetric flow rate, pressure gradient and wall shear stress. The study shows that for a given yield stress, both the nanofluid velocity reduce, as the strength of the magnetic field is increased, but the velocity of the nanofluid increase with the rise in permeability parameter (k). The effect of the wall tension, wall damping and wall elastic on the velocity has been studied. With damping, the velocity increases. Through the analysis, we obtained that the yield stress increases the velocity. The effects of amplitude ratio δ on the complicated behavior of streamlines have been discussed. With increasing the magnetic field and the yield stress, the streamlines are strongly crowded. The pressure difference along the artery affects the tension in the wall of artery, the damping of the wall and the amplitude ratio, where the wall tension or the amplitude ratio increases, pressure difference increases. The study will be useful for dealing with problems related to blood flow in arteries in a pathological state, where the lumen of the artery has turned into a porous structure due to formation of blood clots.