Mathematical Modelling of Sickle-Cell-Induced Variable Viscosity Effects on Magnetohydrodynamic Blood Flow Through a Stenosed Artery with Heat and Mass Transfer

Sickle cell disease is associated with abnormal erythrocyte deformation and altered blood rheology, which may increase resistance to blood flow and contribute to impaired tissue perfusion. The presence of arterial stenosis can further modify the haemodynamic environment and intensify flow resistance. This study develops a mathematical model to investigate the effects of sickle-cell-induced variable viscosity on magnetohydrodynamic blood flow through a stenosed artery in the presence of heat and mass transfer. Blood is modelled as an incompressible, electrically conducting fluid flowing through a symmetric stenosed arterial segment represented within a porous-medium framework. The formulation incorporates concentration-dependent variable viscosity, magnetic resistance, Darcy resistance, thermal and concentration buoyancy, heat transfer, mass diffusion and a prescribed pressure gradient. Appropriate dimensionless variables are introduced to transform the governing momentum, energy and concentration equations into a dimensionless form. A perturbation approach is employed to obtain an analytical expression for the velocity distribution, while the temperature and concentration equations are solved subject to symmetry and wall boundary conditions. Numerical evaluations of the analytical solution are presented using velocity profiles and two-dimensional contour plots for different values of the pertinent parameters. The results show that increasing the favourable pressure gradient, permeability, thermal buoyancy, and concentration buoyancy generally enhances blood velocity. In contrast, increasing magnetic intensity and the sickle-cell-related variable-viscosity contribution suppress the velocity field. Increasing stenosis severity increases flow resistance and generally reduces the overall velocity under the prescribed pressure-gradient condition. The mass-transfer parameter produces comparatively moderate changes in the velocity distribution, while the thermal parameter exhibits stronger sensitivity within particular parameter ranges. The study provides a theoretical framework for understanding the coupled effects of abnormal blood rheology, arterial constriction, magnetic interaction, heat transfer and species transport in sickle-cell-related haemodynamics.