Impact of Thermal and Hemodynamic Factors on Blood Flow in Magnetized Arteries: A Mathematical Perspective (Published)
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.
Keywords: Artery, Hypertension, Temperature, blood pressure, cardiovascular diseases., hypotension, magnetic field
Analysis of Unsteady Blood Flow Through a Stenosed Artery with Constant and Variable Viscosities (Published)
This paper presents a theoretical study of the analysis of unsteady blood flow with constant and variable viscosities through a stenosed artery using a third grade fluid model. Incorporated into the models are the slip velocity and externally applied magnetic field. The methods employed in solving the equations governing the unsteady blood flow models with constant and variable viscosities are the Galerkin’s weighted residual and Forth order Runge-Kutta. Important flow parameters such as flow velocity, flow rate, shear stress and flow resistance have been computed. Graphical representation shows that, for both cases of unsteady blood flow models with constant viscosity and variable viscosity, magnetic field and shear thinning increases with flow resistance but decreases the flow velocity, flow rate and shear stress. Increases in slip velocity and shear thinning lead to increases in flow velocity, flow rate and shear stress but decrease the flow resistance. Other parameters that can positively influence the flow velocity are the pressure gradient and Reynold number. Finally, the velocity profile of unsteady blood flow model with constant viscosity is higher than that with variable viscosity.
Keywords: Unsteady blood flow, Variable viscosity, constant viscosity, magnetic field, slip velocity, stenosed artery, third grade fluid model and Galerkin’s Weighted residual methods.
Analysis of Unsteady Blood Flow through A Stenosed Artery with Constant and Variable Viscosities (Published)
This paper presents a theoretical study of the analysis of unsteady blood flow with constant and variable viscosities through a stenosed artery using a third grade fluid model. Incorporated into the models are the slip velocity and externally applied magnetic field. The methods employed in solving the equations governing the unsteady blood flow models with constant and variable viscosities are the Galerkin’s weighted residual and Forth order Runge-Kutta. Important flow parameters such as flow velocity, flow rate, shear stress and flow resistance have been computed. Graphical representation shows that, for both cases of unsteady blood flow models with constant viscosity and variable viscosity, magnetic field and shear thinning increases with flow resistance but decreases the flow velocity, flow rate and shear stress. Increases in slip velocity and shear thinning lead to increases in flow velocity, flow rate and shear stress but decrease the flow resistance. Other parameters that can positively influence the flow velocity are the pressure gradient and Reynold number. Finally, the velocity profile of unsteady blood flow model with constant viscosity is higher than that with variable viscosity.
Keywords: Unsteady blood flow, Variable viscosity, constant viscosity, magnetic field, slip velocity, stenosed artery, third grade fluid model and Galerkin’s Weighted residual methods.