RADIATION-BRINKMAN NUMBER EFFECTS ON BLOOD FLOW IN A POROUS ATHEROSCLEROTIC MICROCHANNEL WITH THE PRESENCE OF A MAGNETIC FIELD, GROWTH RATE AND TREATMENT
Abstract
Mathematical models representing blood flow through a microchannel with the effect of radiation-Brinkman number with an external magnetic field were formulated. The atherosclerosis is due to an exponential growth of cholesterol in the blood and trans fat consumption. The geometry of atherosclerosis was assumed to be growth rate and time dependent. The blood flow is considered nonlinear, incompressible, viscous, and fully developed. The nonlinear equations under suitable boundary conditions were scaled to a system of dimensionless PDE, which were reduced further to ordinary differential equations using the perturbation conditions. The perturbed system of ordinary differential equations was solved using the Laplace method. The blood flow profiles, such as velocity, volumetric flow rate, lipid concentration profiles such as lipid concentration and rate of mass of the lipid transfer, and temperature profiles such as blood temperature and the rate of heat transfer are obtained and the effects of the pertinent parameters such as magnetic field, radiation absorption, and Brinkman Number were discussed. The results show that the velocity increases with an increase in Brinkman number, Grashof number, solutal Grashof number and the porosity, while it decreases with an increase in Schmidt number, Prandtl number, radiation absorption, chemical reaction, and magnetic field. From the investigation, we could deduce that there is an increase in blood temperature with the increase in Brinkman number and a decrease in temperature due to an increase in Schmidt number, Prandtl number, radiation absorption, chemical reaction, and oscillatory frequency. In conclusion, we have been able to formulate a mathematical representation of blood flow through a sclerotic microchannel, obtained an exact solution to the problem, and presented results that might be useful for mathematicians and clinicians.
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