Impact of Forchheimer Drag and Thermal Transfer in Blood Flow of a Stenosed Artery

Abstract

This research effort presents an extensive investigation of unsteady magnetohydrodynamic (MHD) blood flow in an inclined, stenosed artery embedded with porous medium, non-Newtonian, incompressible, pulsatile and Herschel–Bulkley fluid (HBF) model. Human Blood is simulated as incompressible Herschel–Bulkley (HB) blood flow model to encompass shear thinning (viscosity reduction) or thickening (dilatant behavior) of blood and the effect of yield stress is observed in physiological conditions. The arterial wall is assumed to be the tapered and scheme incorporates Darcy and nonlinear Forchheimer drag forces to simulate realistic flow resistance within biological tissues. The governing equations of the present study consisting of coupled nonlinear partial differential equations (PDEs) are formulated using cylindrical coordinates and solved numerically by finite difference method (FDM). A parametric sensitivity analysis is performed to systematically evaluate the influence of essential dimensionless parameters on hemodynamic and thermal characteristics. The specific effects of the arterial inclination angle, Hartmann number ([Formula: see text]), consistency index ([Formula: see text]), power-law index ([Formula: see text]), yield stress ([Formula: see text]), the influence of the Forchheimer drag coefficient ([Formula: see text]) on the axial velocity distribution and wall shear stress are examined. The effects of the Eckert number ([Formula: see text]) and Prandtl number ([Formula: see text]) in influencing the temperature profile inside the stenosed arterial segment are rigorously examined. These results have considerable significance for improving clinical diagnostic and therapeutic approches for illnesses related to stenosed arteries.