The velocity slip of polar fluids

Brunn, P. O.

doi:10.1007/bf01515899

Cited by 60 publications

(37 citation statements)

References 15 publications

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“…But the usual no-slip condition at the boundary must be changed by the slip condition (Ebart and Sparrow, 1965). Some authors (Brunn, 1975, Nubar, 1971 suggested the existence of a red blood cell slip at the vessel wall. Misra and Kar (1989) developed a momentum integral method to study the problem of blood vessel in the present of a stenosis by taking into consideration the slip velocity at the wall.…”

Section: Frontiers In Heat and Mass Transfermentioning

confidence: 99%

Magnetohydro Dynamic Flow of Blood in a Permeable Inclined Stretching Surface With Viscous Dissipation, Non-Uniform Heat Source/Sink and Chemical Reaction

Reddy¹,

Reddy²,

Suneetha³

2018

Frontiers in Heat and Mass Transfer

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Present work aims to investigate the blood stream in a permeable vessel in the presence of an external magnetic field with heat and mass transfer. The instability in the coupled flow and temperature fields is considered to be produced due to the time-dependent extending velocity and the surface temperature of the vessel. The non-uniform heat source/sink effects on a chemically responded blood stream and heat viscous. This study is of potential value in the clinical healing of cardiovascular disorders accompanied by accelerated circulation. The problem is treated mathematically by reducing it to a system of joined non-linear differential equations, which have been solved by utilizing similarity transformation and boundary layer approximation. The resultant non-linear coupled ordinary differential equations are solved numerically by utilizing the fourth order Runge-Kutta method with shooting technique. Computational results are gotten for the velocity, temperature, the skin-friction coefficient, the rate of heat transfer and rate of mass transfer in the vessel. The evaluated results are compared with another analytical study reported earlier in scientific literatures. The present investigation exposes that the heat transfer rate is upgraded as the value of the unsteadiness parameter increases, but it decreases for the increment of the space reliance parameter for heat source/sink.

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Section: Frontiers In Heat and Mass Transfermentioning

confidence: 99%

Magnetohydro Dynamic Flow of Blood in a Permeable Inclined Stretching Surface With Viscous Dissipation, Non-Uniform Heat Source/Sink and Chemical Reaction

Reddy¹,

Reddy²,

Suneetha³

2018

Frontiers in Heat and Mass Transfer

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“…As r changes with concentration [18], naturally N and L will change with concentration, hence they are interrelated. But in the models given in [16,19] and many others this interrelation is not mentioned. In the present paper we derive the relation between N and L. A non-zero couple stress boundary condition is preferred by Chaturani [12], Kline et al [17], Erdogan [20] and Chaturani and Mahajan [23].…”

Section: Introductionmentioning

confidence: 84%

“…being ignored. Brunn [19] proposed a velocity slip boundary condition. The effects of velocity slip on the apparent viscosity were studied and the restrictions on slip for the occurrence of the sigma phenomenon obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Since rheological properties and the flow behaviour of blood are of immense importance in the fundamental understanding, treatment and diagnosis of many diseases and are different in different regions of circulation, many researchers have proposed different mathematical models [11][12][13][14][15] for blood flow. In the present problem, we shall consider the four blood flow models given by Cowin [16], Kline et al [17], Ariman et al [18] and Brunn [19] for a comparative study.…”

Section: Introductionmentioning

confidence: 99%

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A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

Chaturani

Biswas

1984

Rheol Acta

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In this paper, Poiseuille flow of a polar fluid (model of a red blood cell suspension) under various boundary conditions at the wall, viz., slip or no-slip in the axial velocity and couple stresses zero or non-zero at the boundary, is considered from the point of view of its applications to blood flow. Analytic expressions for axial and rotational velocities, flow rate, effective viscosity and stresses are obtained. The magnitudes of the length ratio L and the coupling number N are determined in accordance with concentration and tube radius (in the existing literature, values of L and N are chosen arbitrarily). Velocity profiles (both axial androtational) and the variation of the effective viscosity with concentration, tube radius and for various values of the boundary condition parameters are shown graphically. The analytic results obtained are compared with experin~ental results (for blood flow). It is found that they are in a reasonably good agreement. The effective viscosity exhibits the Inverse Fahraeus-Lindquist Effect in all the cases (including the slip or no-slip in the velocity fields). A method is given for determining the non-zero couple stress boundary condition for a given concentration. Applications of this theory to blood flow are briefly discussed.

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“…Misra and Shit [23] carried out the role of slip velocity in blood flow through stenosed arteries. Several authors [24,25] suggested the presence of a red blood cell occurring in slip condition at the vessel wall. Recently, Ponalagusamy [26] and Biswas and Chakraborty [27,28] have developed mathematical models for blood flow through stenosed arterial segment, by taking a velocity slip condition at the constricted wall.…”

Section: Introductionmentioning

confidence: 99%

Slip Effects on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration

Sinha

Shit

Kundu

2013

ISRN Biomedical Engineering

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A theoretical investigation concerning the influence of externally imposed periodic body acceleration on the flow of blood through a time-dependent stenosed arterial segment by taking into account the slip velocity at the wall of the artery has been carried out. A mathematical model is developed by treating blood as a non-Newtonian fluid obeying the Casson fluid model. The pulsatile flow is analyzed by considering a periodic pressure gradient and the inertial effects as negligibly small. A suitable generalized geometry for time-dependent stenosis is taken into account. Perturbation method is used to solve the coupled implicit system of nonlinear differential equations that govern the flow of blood. Analytical expressions for the velocity profile, volumetric flow rate, and wall shear stress are obtained. A thorough quantitative analysis has been made through numerical computations of the variables involved in the analysis that are of special interest in this study. The computational results are presented graphically. The results for different values of the parameters involved in the problem under consideration presented here show that the flow is appreciably influenced by slip velocity in the presence of periodic body acceleration.

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The velocity slip of polar fluids

Cited by 60 publications

References 15 publications

Magnetohydro Dynamic Flow of Blood in a Permeable Inclined Stretching Surface With Viscous Dissipation, Non-Uniform Heat Source/Sink and Chemical Reaction

Magnetohydro Dynamic Flow of Blood in a Permeable Inclined Stretching Surface With Viscous Dissipation, Non-Uniform Heat Source/Sink and Chemical Reaction

A comparative study of poiseuille flow of a polar fluid under various boundary conditions with applications to blood flow

Slip Effects on Pulsatile Flow of Blood through a Stenosed Arterial Segment under Periodic Body Acceleration

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