Effect of the rotation,magnetic field and initial stress on peristaltic motion of micropolar fluid

In this work, the effect of magnetic field, rotation and initial stress on peristaltic motion of micropolar fluid in a circular cylindrical flexible tube with viscoelastic or elastic wall properties has been considered. Runge–Kutta technique are used. Runge–Kutta method is developed to solve the governing equations of motion resulting from a perturbation technique for small values of amplitude ratio. The time mean axial velocity profiles are presented for the case of free pumping and analyzed to observe the influence of wall properties, magnetic field, rotation and initial stress for various values of micropolar fluid parameters. In the case of viscoelastic wall, the effect of viscous damping on mean flow reversal at the boundary is seen. The numerical results of the time mean velocity profile are discussed in detail for homogeneous fluid under the effect of wall properties, magnetic field, initial stress and rotation for different cases by figures. The results indicate that the effect of wall properties, rotation, initial stress and magnetic field are very pronounced. Numerical results are given and illustrated graphically.     

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.     

Performance modeling and analysis of blood flow in elastic arteries

Nomenclature　　τ　　wallshearstressγshearrateτy yieldstressηc Cassonviscosityktheconsistencyindexnnon_Newtonianindexτp shearstressofthepthelementωangularvelocityRvessel’sradiusCwavespeedM　　magneticparameter (Hartmannnumber)u,w　velocitycomponentinther_andz_directions,respectivelyP　　pressureα　　unsteadinessparameter k , R meanparametersTp relaxationtimeofthepthelementρ densityIntroductionTheimportancetoatherogenesisofarterialflowphenomenasuchasflowseparation ,recirculationands…     

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied.The analytical solutions of the velocity and microrotation are derived under the Debye-H(u|¨)ckel approximation.The effects of the related dimensionless parameters,e.g.,the micropolar parameter,the frequency,the electrokinetic width,and the wall zeta potential ratio of the upper plate to the lower plate,on the electroosmotic velocity and microrotation are investigated.The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1.The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid.However,the dependence of the microrotation on the related parameters mentioned above is complex.In order to describe these effects clearly,the dimensionless microrotation strength and the penetration depth of the microrotation are defined,which are used to explain the variation of the microrotation.In addition,the effects of various parameters on the dimensionless stress tensor at the walls are studied.     

化学反应对竖直平板边界磁流体动力学微极流体滑流的影响

Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Wall friction effects and viscosity reduction of gel propellants in conical extrusion

Influence of wall friction on mean apparent viscosity reduction of gel propellants in conical radial flow extrusion is investigated analytically and numerically. A parametric study has been conducted to evaluate the effects of injector geometry, rheological constants, wall friction factor and volumetric flow rate on fluid viscosity profile. Gel propellants were modeled by the non-Newtonian power law constitutive relation. The influence of wall friction on the mean apparent viscosity, on wall slip and on pressure gradient is found to be substantial. Central results are supported by asymptotic analysis for small cone angles and low wall friction. Contact is made with lubrication type flow pattern.     

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall she...     

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.     

Peristaltic motion of a non-Newtonian fluid

Summary To understand theoretically the flow properties of physiological fluids, we have considered as a model the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall. The solution for the stream function is obtained as a power series in terms of the amplitude of the wave. The stream function and the velocity components are evaluated by solving numerically two point boundary value problems with a singular point at the origin. The influence of the applied pressure gradient along with non-Newtonian parameters on the streamlines and velocity profiles are discussed in detail.     

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.     

Wave propagation in an elastic tube: a numerical study

In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors.     

On the Generation of Discontinuous Shearing Motions of a Non-Newtonian Fluid

The system under study models unsteady, one-dimensional shear flow of a highly elastic and viscous incompressible non-Newtonian fluid with fading memory under isothermal conditions. The flow, in a channel, is driven by a constant pressure gradient, is symmetric about the center line, and satisfies a no-slip boundary condition at the wall. The non-Newtonian contribution to the stress is assumed to obey a differential constitutive law (due to Oldroyd, Johnson & Segalman), the key feature of which is a non-monotone relation between the total steady shear stress and strain rate. In a regime in which the Reynolds number is much smaller than the Deborah (or Weissenberg) number, one obtains a degenerate, singularly perturbed system of nonlinear reaction-diffusion equations. It is shown that if the driving pressure gradient exceeds a critical value (the local shear stress maximum of the steady stress vs. strain rate relation), then the solution to the governing system, starting from rest at , tends as to a particular discontinuous steady state solution (the “top-jumping” steady state), except in a small neighborhood of the discontinuity. This discontinuous steady state is shown to be nonlinearly stable in a precise sense with respect to perturbations yielding smooth initial data. Such discontinuous steady states have been proposed to explain “spurting” flows, which exhibit a large increase in mean flow rate when the driving pressure is raised above a critical value. (Accepted April 22, 1996)     

Unsteady processes in the neighborhood of a well in the case of a nonlinear flow law and determination of stratum parameters

A study is made of the propagation of disturbances in the neighborhood of a well in the case of a linear elastic regime for a flow law with limiting gradient, and also for a nonlinear elastic regime for different forms of the flow law. The obtained results are used to investigate the difference between two forms of flow anomaly — nonlinearity of the flow law associated with non-Newtonian behavior of the fluid and a pressure dependence of the parameters of the nonlinear flow law due to nonlinear elastic deformations of strata [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–70, July–August, 1983.I thank V. M. Entov and L. A. Chudov for helpful advice and discussion.     

Stokes flow through a permeable tube

Pressure-driven Stokes flow through a circular tube with a permeable wall is considered as a model of blood flow through a capillary vessel. Fluid penetrates the tube wall over a test section according to Starling law relating the normal fluid velocity to the transmural pressure defined as the difference between the wall and the uniform ambient pressure. The problem is formulated using the integral representation for Stokes flow, and the solution is computed with high accuracy using a boundary-element method for specified values of the wall permeability and percentage of fluid escaping through the walls. The results illustrate the structure of the flow and validate the predictions of a model based on the assumption of locally unidirectional flow for sufficiently small permeability.     

Two-phase fluid flow in a porous tube: a model for blood flow in capillaries

A theoretical study of blood flow, under the influence of a body force, in a capillary is presented. Blood is modeled as a two-phase fluid consisting of a core region of suspension of all erythrocytes, represented by a micropolar fluid and a plasma layer free from cells modeled as a Newtonian fluid. The capillary is modeled as a porous tube consisting of a thin transition Brinkman layer overlying a porous Darcy region. Analytical expressions for the pressure, microrotation, and velocities for the different regions are given. Plots of pressure, microrotation, and velocities for varying micropolar parameters, hydraulic resistivity, and Newtonian fluid layer thickness are presented. The overall system was found to be sensitive to variations in micropolar coupling number. It was also discovered that high values of hydraulic resistivity result in an overall slower velocity of the micropolar and Newtonian fluid.     

One-Dimensional Interaction of a Cylindrical Unloading Wave with a Moving Elastic–Plastic Boundary

The one-dimensional dynamic problem of the theory of large elastic–plastic deformations is considered for the interaction of an unloading wave with an elastic–plastic boundary. It is shown that before the occurrence of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elasti©viscoplastic material filling the round tube, which is retained in the tube due to friction on its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment of the onset of slippage of the material along the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.     

Conjugate heat transfer within a concentric annulus filled with micropolar fluid

This paper investigates numerically the conjugate heat transfer in an annulus between two concentric cylinders. The annulus contains micropolar fluid and is heated isothermally from its inner wall. The effect of Rayleigh number, thickness of inner wall, inner wall-fluid thermal conductivity ratio, and material parameters of micropolar fluid on heat transfer rate within the annulus has been investigated. The study has shown that for low Rayleigh number regimes and for thermal conductivity of the inner wall greater than that of the fluid, the increase of inner wall thickness increases the heat transfer rate through the annulus and vice versa. While for convection dominating regimes Ra ≥ 10⁴ the increase of inner wall thickness decreases the heat transfer rate. Moreover, the study has shown that for fixed geometrical and flow parameters the heat transfer decreases in case of micropolar fluids in comparison with that of Newtonian fluids.