Partial differential equation in blood circulation
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Explanation:
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Blood flow is a study of measuring the blood pressure and finding the flow through the blood vessel. Blood flow problem has been studied for centuries where one of the motivations was to understand the conditions that contribute to high blood pressure. This occurs when the blood vessel became narrowed from its normal size. This paper presents a mathematical modeling of the arterial blood flow which was derived from the Navier-Stokes equations and some assumptions. A system of nonlinear partial differential equations for blood flow and the cross-sectional area of the artery was obtained. Finite difference method was adopted to solve the equations numerically. The result obtained is very sensitive to the values of the initial conditions and this helps to explain the condition of hypertension. Blood flow is a study of measuring the blood pressure and finding the flow through the blood vessel. This study is important for human health. Most of the researches study the blood flow in the arteries and veins. One of the motivations to study the blood flow was to understand the conditions that may contribute to high blood pressure. Past studies indicated that one of the reasons a person having hypertension is when the blood vessel becomes narrow. This paper will focus on the diastolic hypertension. Blood is non-Newtonian fluid and to model such fluid is very complicated. In this problem, blood is assumed to be a Newtonian fluid. Even though this will make the problem much simpler, it still is valid since blood in a large vessel acting almost like a Newtonian fluid. In order to model this problem, Navier- Stokes equations will be used to derive the governing equations that represent this problem.