锥形狭窄动脉血流非牛顿Reiner-Rivlin模型的分析研究

N. Dash, Sarita Singh
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引用次数: 1

摘要

Аbstract。狭窄,即动脉的异常狭窄,由于对血液流动的阻力增加而显著影响血流动力学。血流速度、动脉压分布、管壁剪切应力和阻力阻抗因子在不同狭窄程度下发生变化。预先了解病变动脉的流速、流速、压降等血流参数对预防和治疗性医疗干预至关重要。本文给出了考虑Reiner - Rivlin流体本构关系的轴对称稳态情况下Navier - Stokes质量动量守恒方程的解。Reiner - Rivlin本构关系将守恒方程转化为非线性偏微分方程。文献中很少报道半解析解和数值解,但没有发现解析解。这促使本研究寻求考虑Reiner - Rivlin本构关系的闭型解。求解得到轴向速度表达式,以体积流量为初始条件,利用轴向速度表达式可得到压力梯度、阻力阻抗和壁面剪应力。研究了粘度、交叉粘度、流量、动脉锥角和狭窄程度对轴向速度、阻力阻抗和管壁剪应力的影响。
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Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery
Аbstract. Stenosis, the abnormal narrowing of artery, significantly affects dynamics of blood flow due to increasing resistance to flow of blood. Velocity of blood flow, arterial pressure distribution, wall shear stress and resistance impedance factors are altered at different degree of stenosis. Prior knowledge of flow parameters such as velocity, flow rate, pressure drop in diseased artery is acknowledged to be crucial for preventive and curative medical intervention. The present paper develops the solution of Navier – Stokes equations for conservation of mass and momentum for axis-symmetric steady state case considering constitutive relation for Reiner – Rivlin fluid. Reiner – Rivlin constitutive relation renders the conservation equations nonlinear partial differential equations. Few semi-analytical and numerical solutions are found to be reported in literature but no analytical solution. This has motivated the present research to obtain a closed-form solution considering Reiner – Rivlin constitutive relation. Solution yields an expression for axial velocity, which is utilized to obtain pressure gradient, resistance impedance and wall shear stress by considering volumetric flow rate as initial condition. The effect of viscosity, cross viscosity, flow rate, taper angle of artery and degree of stenosis on axial velocity, resistance impedance and wall shear stress are studied.
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来源期刊
Mathematical Biology and Bioinformatics
Mathematical Biology and Bioinformatics Mathematics-Applied Mathematics
CiteScore
1.10
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发文量
13
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