Mathematical Modeling of the Impact of Temperature and Elevated Sickle Cell Concentration on MHD Blood Flow Through a Porous Atherosclerotic Channel

Abstract

This study offers a comprehensive mathematical and computational investigation of the combined effects of temperature gradient and high sickle cell concentration on blood circulation through a porous atherosclerotic channel in the presence of an applied magnetic field. The model incorporates key physiological and physical mechanisms, including magnetohydrodynamics (MHD), heat transfer, mass transport, porous medium resistance, and chemical reaction effects, to simulate realistic blood flow behavior under pathological conditions. The governing equations for momentum, energy, and concentration were formulated using appropriate assumptions for incompressible, electrically conducting blood flow. These equations were non-dimensionalised to identify important controlling parameters such as the Hartmann number (magnetic field strength), Grashof number (thermal buoyancy), solutal Grashof number (concentration buoyancy), Prandtl number, Schmidt number, porosity parameter, and chemical reaction parameter. Analytical methods were employed to obtain solutions, which were further analyzed through graphical and computational techniques. The results reveal that increased sickle cell concentration significantly increases flow resistance, leading to a reduction in velocity and impaired blood circulation, particularly in the presence of arterial narrowing due to atherosclerosis. The temperature gradient plays a dual role: it enhances fluid motion through buoyancy effects while also influencing viscosity and thermal diffusion. The applied magnetic field introduces a Lorentz force that suppresses fluid velocity, thereby providing a potential mechanism for controlling abnormal blood flow. The study demonstrates that the interaction between magnetic field, temperature gradient, and sickle cell concentration has a significant impact on blood flow characteristics in porous, diseased arteries. This work contributes to the advancement of biomedical fluid dynamics by offering a more realistic model for analyzing blood flow in pathological environments. It has potential applications in the design of medical treatments, such as magnetic field-assisted therapy, targeted drug delivery, and improved diagnostic understanding of circulatory disorders associated with sickle cell disease and atherosclerosis.