Mathematical Modelling of the Thermosolutal Effect on Blood Flow through a Micro-Channel in the Presence of a Magnetic Field

Abstract

Substances such as mass concentrations in the blood cause circulation challenges. Blood is a substance made up of 55% plasma and 45% hemoglobin, which flows through the blood vessels and is aided by the heart in pumping to all organs and other tissues and cells in the human body. Mathematical modelling plays an important role in understanding the blood circulation problem in the human body, and it helps transform the real-life cardiovascular problem into a system of mathematical equations. In this research, we transformed the real-life cardiovascular problem of the heat effect on mass concentration and blood flow through blood vessels into a system of partial differential equations representing blood momentum, energy, and mass concentration equations after modifying the Navier-Stoke equation. The models are scaled from dimensional to dimensionless using specific scaling parameters. The scaled dimensionless equations were further perturbed and reduced to a system of ordinary differential equations, and the system of ODEs was solved using the Laplace method, where mathematical models representing blood velocity profiles, temperature profiles, and mass concentration profiles were obtained. A numerical simulation was performed using Wolfram Mathematica, version 12, where the effect of the pertinent parameters on the flow profiles was investigated and the results were presented graphically. The variation of the pertinent parameters such as the Grashof number, solutal Grashof number, Prandtl number, Soret number, Schmidt number, Darcy number, and magnetic field affect the flow profile such that the increase in Grashof number and solutal Grashof number causes the blood velocity to increase substantially at the centre of the vessel before decreasing to zero as the wall boundary layer increases, while the increase in Prandtl number and Soret number increases the blood temperature and velocity.