Asian Journal of Pure and Applied Mathematics

In this study, convective fluid flow through a sclerotic oscillatory artery in the presence of radiative heat and a magnetic field was conceived and formulated as a partial differential equation subject to a no-slip boundary condition. The magnetic field is assumed to be constant and perpendicular to the flow of blood in an artery, where the blood is assumed to be a viscous, incompressible, electrically conducting fluid. The system of partial differential equations was scaled to be a dimensionless system and was further reduced to a system of ordinary differential equations using the perturbation method, where we obtained some governing parameters involved. The Laplace method was used to obtain the analytical solution to the governing models. Analytical and explicit expressions of the axial velocity, temperature profile, and lipid concentration profile are obtained and numerical simulation is carried out using Wolfram Mathematica in order to demonstrate the effect of the obtained pertinent parameters on the flow profiles and to show the applicability of the formulated mathematical models. The results showed that the axial velocity is maximum at the centre of the sclerotic artery where the radius is zero; however, the velocity begins to decrease as the wall thickness increases for different wall temperatures and lipid concentrations. The aforementioned behavior was seen for Schmidt number, chemical reaction parameter, thermal Grashof number, the lipid concentration growth rate, and stenotic height increase, but the velocity profile showed a reversing flow when there is an increase in radiation absorption, magnetic field due to Lorentz force, and systolic pressure parameter. Secondly, it is seen that an increase in wall temperature increases blood temperature. This is because the additional temperature increases the fluid convection; the lipid growth rate also increases the fluid temperature. However, the temperature of the fluid decreases for an increase in Prandtl number, radiation absorption parameter, oscillatory frequency. Thirdly, the investigation involved the role played by the lipid concentration on the fluid; it is seen that wall lipid concentration, growth rate, and stenotic height increase in turn increase the lipid concentration profile, but the concentration profile decreases for an increase in Schmidt number, chemical reaction, and oscillatory frequency parameter. This research has shown that blood flow through a sclerotic artery can be modeled and is useful in understanding blood flow problems. This could lead to more cardiovascular issues and, as such, is a useful guide for mathematicians and scientists who would be interested in understanding and proffering solutions to blood flow problems.