The study of Vorticity for Two-Layered Magnetohydrodynamic Flow through Parallel Plates

Abstract

This paper investigates the vorticity characteristics within a two-layered Magnetohydrodynamic (MHD) model applied to a parallel plate hemodialyzer subjected to a uniform transverse magnetic field. Analytical expressions for the vorticity are derived for both the core fluid region and the peripheral plasma layer. These expressions are subsequently analyzed to obtain vorticity profiles as a function of the Hartmann number (M), with the thickness of the peripheral plasma layer (δ) held constant. The study reveals that, as the Hartmann number increases, the flow of the suspension exhibits a tendency to reduce the cell-free zone near the wall, while the plasma exposure area to the membrane increases. This results in a complex vorticity behavior where effective vorticity initially decreases and then increases with rising Hartmann number (M). The findings suggest that these MHD effects can be leveraged to optimize energy management and mitigate the risks of red blood cell injury, such as blood clotting, near the membrane wall during the dialysis process. This work provides a novel insight into the role of magnetic fields in enhancing the hemodialysis process through improved flow dynamics.