Hydromagnetic blood flow through a channel of varying width bounded by porous media of finite thickness

Abstract

This study examines hydromagnetic blood flow through a channel with a varying width, bounded by porous media of finite thickness, using the Beavers–Joseph–Rudraiah slip conditions. In this context, the channel models blood flow, while the surrounding porous wall represents the tissue space. By utilizing power series approximations related to the wall slope, analytical expressions for flow characteristics including axial velocity in the x and y directions, wall momentum flux, resistance force, and shear stress are derived. These results are subsequently used to analyze blood flow through a smooth constriction surrounded by porous walls. The discussion centers on the effects of the magnetic field, slip parameter, and the width of the porous wall on flow resistance and the distribution of wall shear stress, while comparing these results with the Beavers–Joseph slip conditions. It is observed that flow resistance decreases with an increasing Hartmann number across different values of the porous parameter, which is consistent with the expectation that stronger magnetic fields reduce fluid motion and resistance. Moreover, shear stress decreases with a higher Hartmann number but increases with a larger porous parameter. Both the resistance force and shear stress are also influenced by the width of the porous walls. These findings have practical implications, particularly for evaluating the performance of prosthetic devices within the human body.