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Mathematical modeling of non-Newtonian fluid in arterial blood flow through various stenoses
Advances in Difference Equations ( IF 4.1 ) Pub Date : 2021-07-16 , DOI: 10.1186/s13662-021-03492-9
Pinyo Owasit 1, 2 , Somchai Sriyab 2, 3
Affiliation  

Since the stenosis geometry of some cardiovascular patients cannot be described by a vertically symmetric function throughout the stenosis, so it motivates us to study the blood flow through a vertically asymmetric stenosis. In addition, we compare the flow quantities in bothvertically symmetric and asymmetric stenoses. The vertically symmetric stenosis is explained by a vertically symmetric function such as an exponential function in bell shape and a cosine function in cosine shape. The vertically asymmetric stenosis is interpreted by a vertically asymmetric function such as the combination of two different stenosis shapes. Blood is treated as a non-Newtonian fluid which is represented in the power-law model. The finite difference scheme is used to solve governing equations for obtaining the flow quantities such as axial velocity, radial velocity, flow rate, resistance to flow, and skin friction. We investigated the way that the stenosis height, stenosis length, and non-Newtonian behavior affect the flow quantities through three various stenoses. The flow quantities in the bell shape and cosine shape of stenosis show significantly different behavior. Moreover, we found that the flow quantities in the single shape (bell shape or cosine shape) have the same behavior as the flow quantities in the combined shape in the first half part, but have a slightly different behavior in the last half part.



中文翻译:

通过各种狭窄的动脉血流中的非牛顿流体的数学模型

由于某些心血管患者的狭窄几何形状不能用贯穿狭窄的垂直对称函数来描述,因此它促使我们研究通过垂直不对称狭窄的血流。此外,我们比较了垂直对称和非对称狭窄中的流量。垂直对称狭窄由垂直对称函数解释,例如钟形指数函数和余弦形余弦函数。垂直不对称狭窄由垂直不对称函数解释,例如两种不同狭窄形状的组合。血液被视为非牛顿流体,以幂律模型表示。有限差分格式用于求解控制方程以获得轴向速度、径向速度、流速、流动阻力和皮肤摩擦。我们研究了狭窄高度、狭窄长度和非牛顿行为通过三种不同的狭窄影响流量的方式。钟形和余弦形狭窄处的流量表现出明显不同的行为。此外,我们发现单个形状(钟形或余弦形状)中的流量在前半部分与组合形状中的流量具有相同的行为,但在后半部分的行为略有不同。钟形和余弦形狭窄处的流量表现出明显不同的行为。此外,我们发现单个形状(钟形或余弦形状)中的流量在前半部分与组合形状中的流量具有相同的行为,但在后半部分的行为略有不同。钟形和余弦形狭窄处的流量表现出明显不同的行为。此外,我们发现单个形状(钟形或余弦形状)中的流量在前半部分与组合形状中的流量具有相同的行为,但在后半部分的行为略有不同。

更新日期:2021-07-16
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