Mathematical Analysis of Thermal and Hemodynamic Effects on Blood Flow in Magnetized Arteries

Maintaining optimal blood pressure is vital for overall health, as deviations from normal levels can lead to serious complications. Hypertension is known to damage the cardiovascular system and vital organs, while hypotension reduces blood flow, impairing critical bodily functions. Effective management strategies, such as lifestyle modifications, regular monitoring, and medical interventions, are crucial in mitigating these risks. Mathematical modeling plays an integral role in analyzing blood circulation in the human body. By translating real-world cardiovascular challenges into mathematical equations, it enables the study of complex physiological systems. In this research, the combined effects of heat and blood pressure on blood flow through blood vessels were modeled mathematically. The Navier-Stokes equation was modified to develop a system of partial differential equations (PDEs) governing blood momentum and temperature distribution. The system of PDEs was then scaled into a set of dimensionless models and further simplified into Ordinary Differential Equations (ODEs) using oscillatory perturbation parameters. Laplace transformation techniques were employed to solve the governing equations analytically. The resulting flow profiles were simulated numerically using Wolfram Mathematica (Version 12), with variations in key biophysical parameters. Key findings from the simulation include: An increase in the Prandtl number resulted in decreased temperature and velocity profiles. A rise in the Grashof number led to an enhancement in blood velocity. Increasing the oscillatory frequency exhibited a diminishing effect on both temperature and velocity profiles