Nonlinear waves in a viscous fluid contained in a viscoelastic tube

Demı́ray, Hilmi

doi:10.1007/pl00001586

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…В данной работе рассматривается квази-одномерная модель движения жидкости в трубке, которая содержит в себе все основные физические характеристики системы кровь-стенка сосуда. Существенным моментом этой модели является так называемое «гидравлическое приближение» [9,11], при котором предполагается, что осевая компонента скорости течения жидкости много больше, чем радиальная, а на границе выполнено условие равенства нулю компонент скорости. Данное приближение позволяет усреднить уравнения Навье-Стокса и уравнения непрерывности по поперечному сечению сосуда [9,11].…”

Section: система уравнений для описания волн в вязко-эластичных трубкахunclassified

Nonlinear evolution equations for description of perturbations in a viscoelastic tube

Kudryashov¹,

Sinelshchikov²,

Chernyavsky³

2008

Nelin. Dinam.

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Рассмотрена квази-одномерная модель течения жидкости в вязко-эластичной трубке. Предложена замкнутая система нелинейных уравнений для описания возмущений давления и радиуса при течении жидкости в вязкоэластичной трубке. Для анализа системы использованы техника метода многих масштабов и метод возмущений. Математическая модель исследовалась при больших числах Рейнольдса. В уравнении движения стенки трубки учтена кубическая поправка к закону Гука. Построены семейства нелинейных эволюционных уравнений для описания возмущений основных характеристик течения. Найдены точные решения некоторых нелинейных эволюционных уравнений. Ключевые слова: вязко-эластичная трубка, нелинейные эволюционные уравнения, метод многих масштабов, точные решения N. A. Kudryashov, D. I. Sinelshchikov, I. L. Chernyavsky Nonlinear evolution equations for description of perturbations in a viscoelastic tube A quasi-one-dimensional model of flow of a liquid in a viscoelastic tube is considered. A closed system of the nonlinear equations for the description of perturbations of pressure and radius is propose at flow of a liquid in a is viscoelastic tube. For the analysis of system technique of the multiscale method and the perturbation theory is used. The mathematical model was investigated in case of the large Reynolds numbers. In the equation of movement of a wall of a tube the cubic correction to Hooke's law is considered. Families of the nonlinear evolutionary equations for the description of perturbations of the basic characteristics of flow are obtained. Exact solutions of some nonlinear evolution equations are found.

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Section: система уравнений для описания волн в вязко-эластичных трубкахunclassified

Nonlinear evolution equations for description of perturbations in a viscoelastic tube

Kudryashov¹,

Sinelshchikov²,

Chernyavsky³

2008

Nelin. Dinam.

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“…Cox [12] considered the propagation of harmonic pressure waves through a Newtonian fluid contained in a thick-walled, viscoelastic tube as a model of arterial blood flow. Kizilova [13] studied the pressure waves propagation and Demiray [14,15] studied nonlinear waves in viscoelastic tubes. In these works fluid are not considered dusty fluid.…”

Section: Introductionmentioning

confidence: 99%

Propagation of harmonic waves in prestressed fiber viscoelastic thick tubes filled with a viscous dusty fluid

Ergün

Ercengiz

2010

Applied Mathematical Modelling

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a b s t r a c tIn this work, propagation of harmonic waves in initially stressed cylindrical viscoelastic thick tubes filled with a Newtonian fluid is studied. The tube, subjected to a static inner pressure P i and a positive axial stretch k, will be considered as an incompressible viscoelastic and fibrous material. The fluid is assumed as an incompressible, viscous and dusty fluid. The field equations for the fluid are obtained in the cylindrical coordinates. The governing differential equations of the tube's viscoelastic material are obtained also in the cylindrical coordinates utilizing the theory of small deformations superimposed on large initial static deformations. For the axially symmetric motion the field equations are solved by assuming harmonic wave solutions. A closed form solution can be obtained for equations governing the fluid body, but due to the variability of the coefficients of resulting differential equations of the solid body, such a closed form solution is not possible to obtain. For that reason, equations for the solid body and the boundary conditions are treated numerically by the finite-difference method to obtain the effects of the thickness of the tube on the wave characteristics. Dispersion relation is obtained using the long wave approximation and, the wave velocities and the transmission coefficients are computed.

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“…The pulsatile flow of a dusty fluid in an initial stressed thick elastic tube was studied by Ercengiz [11]. Demiray [12,13] investigated nonlinear waves in viscoelastic and elastic tubes. Jagielska et al [14] determined the dispersion relations for thinwalled flexible fluid-filled tube surrounded by an external viscoelastic tissue.…”

Section: Introductionmentioning

confidence: 99%

The Effect of a Residual Stress on Wave Propagation in a Fluid-Filled Thick Elastic Tube

Erol¹

2019

Anadolu University Journal of Science and Technology-a Applied Sciences and Engineering

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The propagation of harmonic waves in an elastic tube filled with fluid is presented in this study. The tube material is considered to be incompressible, homogeneous, isotropic, initially axially stretched, inflated, and constructed of thick elastic, like human arteries. The viscous fluid is assumed to be incompressible and Newtonian. The differential equations of both materials are obtained in cylindrical coordinates. The analytical solutions of the equations of motion for the fluid and numerical solutions of the equations of motion for the tube have been found. The residual circumferential strain in the unloaded state of artery causes an opening angle. The dispersion relation is presented as a function of the axial stretch, opening angle, internal pressure, and material parameters. The effects of these parameters are shown and discussed in the graphics.

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Nonlinear waves in a viscous fluid contained in a viscoelastic tube

Cited by 8 publications

References 10 publications

Nonlinear evolution equations for description of perturbations in a viscoelastic tube

Nonlinear evolution equations for description of perturbations in a viscoelastic tube

Propagation of harmonic waves in prestressed fiber viscoelastic thick tubes filled with a viscous dusty fluid

The Effect of a Residual Stress on Wave Propagation in a Fluid-Filled Thick Elastic Tube

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