European Journal of Applied Physics ISSN: 2684-4451 DOI: http://dx.doi.org/10.24018/ejphysics.2022.4.1.147 Vol 4 | Issue 1 | January 2022 35 Abstract — An attempt was made to investigate an embolitic plaque effect on blood flow through a microchannel and the impact of the magnetic field, metabolic heat, and external heat source on improving blood flow. To address the aforementioned objectives, mathematical models were developed for blood flow and heat transfer with a source. The governing models were scaled using the dimensionless quantities, and the plaque area was derived from Dominguez [28], in which it was incorporated into the governing equations. The governing equations were further reduced to ordinary differential equations using the perturbation method, and the subsequent ordinary differential equations were solved using the method of undermined coefficients, and the constants obtained with the help of the matrix method using the boundary conditions. Furthermore, simulation was carried out to study the effect of the pertinent parameters using Wolfram Mathematica, a computational software. From the simulated results, it is seen that the entering parameters such as magnetic field parameter, the Reynolds number, Womersley number, oscillatory frequency parameter, and permeability parameter all affect the blood velocity and temperature profiles, showing significant impactful results that are useful to both mathematicians and clinicians. Keywords — Embolic, Metabolism, Blood, Magnetic field, Plaque, Oscillatory. I. INTRODUCTION 1 The embolic plaque buildup inside arteries raises the risk of developing cardiovascular disease such as heart attack, stroke, or cholesterol embolism. A cholesterol embolism, also called an atheroembolism or cholesterol embolization syndrome, is when a crystal of cholesterol breaks off a plaque deposit inside one of the arteries. This cholesterol crystal can then travel through your bloodstream and block blood flow in one of the smaller blood vessels or microchannels, causing inflammation. The blockage and inflammation can damage organs or tissues that are supplied by blood vessels. The most commonly affected organs are the kidneys, skin, gastrointestinal system, and the brain, Ghanem et al. [1]. The cardiovascular system is made up of blood cells, blood vessels, and the heart. The main function of the heart is to pump blood into circulation, to the tissues and organs of the human body through the blood vessels. According to Bunonyo and Amos [2], blood is an essential ingredient of the vitality of the body system, and its major constituents are the red blood cells (erythrocytes), white blood cells (leukocytes), platelets, and plasma fluid. Blood contains hemoglobin, which has magnetic properties that are different depending on the oxidation state of hemoglobin. The body contains proteins, such as LDL cholesterol, which when in increasing quantity in the cardiovascular system can build up in various arteries, clogging and reducing their flexibility. Atherosclerosis results in restricted normal blood flow because of the loss of vessel flexibility, so the heart works harder to push blood through to the downstream, Okpeta and Bunonyo [3]. Bio-magnetic fluid dynamics has many major applications, such as magnetic drug targeting, adjusting blood flow during surgery, transporting complex bio-waste fluids, cancer tumor treatment, etc. Extensive research has been undertaken on the fluid dynamics of bio-magnetic fluids under the presence of an external magnetic field. The application of magneto-hydrodynamics in physiological flow is of growing interest as many researchers have reported that blood is an electrically conducting fluid, Singh and Rathee [4]. Over several decades, there have been so many researchers that have worked on blood flow problems; a mathematical modeling of tumor growth in mice following low-level direct electric current was proposed by Cabrales et al. [5]. 1 Submitted on December 28, 2021. Published on January 19, 2022. K. W. Bunonyo, Department of Mathematics and Statistics, Federal University Otuoke, Ogbia, Nigeria. (corresponding e-mail: wilcoxbk @ fuotuoke.edu.ng) L. Ebiwareme, Department of Mathematics, Rivers State University, Port Harcourt, Nigeria Oscillatory Blood Flow and Embolitic Plaque Effect Through a Microchannel with Metabolic Heat and Magnetic Field K. W. Bunonyo and L. Ebiwareme