scholarly journals An Exact Solution for a Boundary Value Problem with Application in Fluid Mechanics and Comparison with the Regular Perturbation Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
S. M. Khaled
Keyword(s):  
Exact Solution ◽  
Perturbation Method ◽  
Axial Velocity ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Jeffrey Fluid ◽  
Regular Perturbation ◽  
Viscosity Parameter ◽  
Axial Velocity Profile

The exact solution for any physical model is of great importance in the applied science. Such exact solution leads to the correct physical interpretation and it is also useful in validating the approximate analytical or numerical methods. The exact solution for the peristaltic transport of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel has been achieved. The main advantage of such exact solution is the avoidance of any kind of restrictions on the viscosity parameterα, unlike the previous study in which the restrictionα≪ 1 has been put to achieve the requirements of the regular perturbation method. Hence, various plots have been introduced for the exact effects of the viscosity parameter, Daray’s number, porosity, amplitude ratio, Jeffrey fluid parameter, and the amplitudes of the waves on the pressure rise and the axial velocity. These exact effects have been discussed and further compared with those approximately obtained in the literature by using the regular perturbation method. The comparisons reveal that remarkable differences have been detected between the current exact results and those approximately obtained in the literature for the axial velocity profile and the pressure rise.

scholarly journals Peristaltic Flow of a Jeffrey Fluid with Variable Viscosity in an Asymmetric Channel

2009 ◽  
Vol 64 (11) ◽  
pp. 713-722 ◽  
Author(s):  
Sohail Nadeem ◽  
Noreen Sher Akbar
Keyword(s):  
Variable Viscosity ◽  
Pressure Rise ◽  
Reynold Number ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Fluid Viscosity ◽  
Asymmetric Channel ◽  
Regular Perturbation ◽  
Viscosity Parameter ◽  
Energy Equations

In this article, we have considered incompressible Jeffrey fluids and studied the effects of variable viscosity in the form of a well-known Reynold’s model of viscosity in an asymmetric channel. The fluid viscosity is assumed to vary as an exponential function of temperature. The governing fundamental equations are approximated under the assumption of long wavelength and low Reynold number. The governing momentum and energy equations are solved using regular perturbation in terms of a small viscosity parameter β to obtain the expressions for stream functions pressure rise and temperature field. Numerical results are obtained for different values of viscosity parameter β , channel width d, wave amplitude b, and Jeffrey parameter λ1. It is observed that the behaviour of the physical parameters λ1, β , and d on pressure rise versus flow rate is as follows: when we increase these parameters pressure rise decreases while pressure rise increases with the increase in b. It is also observed that temperature profile increases when we increase Ec, Pr, and β . Trapping phenomena are also discussed at the end of the article to see the behaviour of different parameters on streamlines

scholarly journals Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
A. Afsar Khan ◽  
R. Ellahi ◽  
K. Vafai
Keyword(s):  
Porous Medium ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Wave Train ◽  
Nonlinear Partial Differential Equations ◽  
Pressure Rise ◽  
Analytic Solutions ◽  
Jeffrey Fluid ◽  
Asymmetric Channel ◽  
Regular Perturbation

The peristaltic flow of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel is investigated. The channel asymmetric is produced by choosing the peristaltic wave train on the wall of different amplitude and phase. The governing nonlinear partial differential equations for the Jeffrey fluid model are derived in Cartesian coordinates system. Analytic solutions for stream function, velocity, pressure gradient, and pressure rise are first developed by regular perturbation method, and then the role of pertinent parameters is illustrated graphically.

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

2020 ◽  
Vol 75 (8) ◽  
pp. 727-738 ◽  
Author(s):  
Ramzy M. Abumandour ◽  
Islam M. Eldesoky ◽  
Mohamed H. Kamel ◽  
Mohamed M. Ahmed ◽  
Sara I. Abdelsalam
Keyword(s):  
Pressure Gradient ◽  
Hartmann Number ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Friction Forces ◽  
Long Wavelength ◽  
Viscosity Parameter ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Theoretical Results

AbstractIn the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

scholarly journals Influence of Variable Viscosity on Peristaltic Motion of a Viscoelastic Fluid in a Tapered Microfluidic Vessel

2018 ◽  
Vol 7 (4.10) ◽  
pp. 49 ◽  
Author(s):  
J. Prakash ◽  
E. P.Siva ◽  
A. Govindarajan ◽  
M. Vidhya
Keyword(s):  
Viscoelastic Fluid ◽  
Axial Velocity ◽  
Variable Viscosity ◽  
Fluid Dynamic ◽  
Wave Train ◽  
Flow Analysis ◽  
Pressure Rise ◽  
Average Pressure ◽  
Peristaltic Motion ◽  
Long Wavelength

The peristaltic flow of a viscoelastic fluid in the tapered microchannel with variable viscosity is investigated. This study is reinvigorated by discovering fluid dynamic in peristaltic motion as signified by biological flows, pharmacodynamics and gastro-intestinal motility enhancement. The microchannel non-uniform and asymmetry is developed by choosing a peristaltic wave train on the wall with different amplitudes and phases. The flow analysis has been arisen for low Reynolds number and long wavelength case. The solutions for stream function, axial velocity and pressure gradient are obtained. The effects of pertinent parameters on the average pressure rise per wavelength are investigated by means of numerical integration. The axial velocity and phenomena of trapping are further discussed.  

Flow in a rotating non-aligned straight pipe

1984 ◽  
Vol 144 ◽  
pp. 297-310 ◽  
Author(s):  
J. Berman ◽  
L. F. Mockros
Keyword(s):  
Velocity Profile ◽  
Axial Velocity ◽  
Reynolds Numbers ◽  
Straight Pipe ◽  
Regular Perturbation ◽  
Axial Velocity Profile ◽  
Axial Profile ◽  
Flow Through ◽  
Effects Of Rotation ◽  
Two Parameters

A third-order regular perturbation solution is developed for laminar flow through a straight pipe that is rotating about an axis not aligned with the pipe axis. Coriolis accelerations produce transverse secondary velocities (similar to those in flow through coiled tubes) and modify the axial-velocity profile. The effects of rotation on the velocity fields are shown to depend on two parameters: (i) the product of axial and rotational Reynolds numbers, and (ii) the square of the rotational Reynolds number itself. Even though their strength increases with increases in parameter magnitudes, transverse circulations are qualitatively insensitive to parametric values. The axial profile, on the other hand, can be significantly modified by the rotation; the zeroth-order parabolic axial profile can be skewed toward the outside, dimpled in the centre with maximums on either side of the centreline, or both, depending on the values of the two parameters. The modification of the axial-velocity profile has important ramifications in the design of heat/mass-transfer devices.

Peristaltic transport of a Jeffrey fluid under the effect of gravity field and rotation in an asymmetric channel with magnetic field

2017 ◽  
Vol 13 (4) ◽  
pp. 522-538 ◽  
Author(s):  
A.M. Abd-Alla ◽  
S.M. Abo-Dahab ◽  
Abdullah Alsharif
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Gravity Field ◽  
Axial Velocity ◽  
Hartmann Number ◽  
Pressure Rise ◽  
Jeffrey Fluid ◽  
Asymmetric Channel ◽  
Mean Flow ◽  
Content Type

Purpose The purpose of this paper is to study the peristaltic flow of a Jeffrey fluid in an asymmetric channel, subjected to gravity field and rotation in the presence of a magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. Involved problems are analyzed through long wavelength and low Reynolds number. Design/methodology/approach The analytical expressions for the pressure gradient, pressure rise, stream function, axial velocity and shear stress have been obtained. The effects of Hartmann number, the ratio of relaxation to retardation times, time-mean flow, rotation, the phase angle and the gravity field on the pressure gradient, pressure rise, streamline, axial velocity and shear stress are very pronounced and physically interpreted through graphical illustrations. Comparison was made with the results obtained in the asymmetric and symmetric channels. Findings The results indicate that the effect of the Hartmann number, the ratio of relaxation to retardation times, time-mean flow, rotation, the phase angle and the gravitational field are very pronounced in the phenomena. Originality/value In the present work, the authors investigate gravity field, and rotation through an asymmetric channel in the presence of a magnetic field has been analyzed. It also deals with the effect of the magnetic field and gravity field of peristaltic transport of a Jeffrey fluid in an asymmetric rotating channel.

scholarly journals Exact Solution for Peristaltic Flow of Jeffrey Fluid Model in a Three Dimensional Rectangular Duct having Slip at the Walls

2014 ◽  
Vol 11 (1-2) ◽  
pp. 81-90 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi ◽  
A. Zeeshan
Keyword(s):  
Exact Solution ◽  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Jeffrey Fluid ◽  
Long Wavelength ◽  
Peristaltic Pumping ◽  
Stream Functions

In the present article, we tried to develop the exact solutions for the peristaltic flow of Jeffrey fluid model in a cross section of three dimensional rectangular channel having slip at the peristaltic boundaries. Equation of motion and boundary conditions are made dimensionless by introducing some suitable nondimensional parameters. The flow is considered under the approximations of low Reynolds number and long wavelength. Exact solution of the obtained linear boundary value problem is evaluated. However, the expression for pressure rise is calculated numerically with the help of numerical integration. All pertinent parameters are discussed through graphs of pressure rise, pressure gradient, velocity and stream functions. It is found that presence of slip at the walls reduces the flow velocity but increases the peristaltic pumping characteristics.

scholarly journals Modeling of Nonlinear Variable Viscosity on Peristaltic Transport of Fluid with Slip Boundary Conditions: Application to Bile Flow in Duct

2021 ◽  
Vol 13 (3) ◽  
pp. 821-832
Author(s):  
S. Kumari ◽  
T. K. Rawat ◽  
S. P. Singh
Keyword(s):  
Boundary Conditions ◽  
Pressure Gradient ◽  
Axial Velocity ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Peristaltic Transport ◽  
Slip Boundary Conditions ◽  
Nonlinear Variation ◽  
Slip Boundary ◽  
Velocity Pressure

The present article deals with variable viscosity on the peristaltic transport of bile in an inclined duct under the action of slip boundary conditions. The wall geometry is described by the sinusoidal wave propagating in the axial direction with different amplitude and with constant speed. The flow of fluid is examined in a wave frame of reference, moving with the velocity of the wave.  Mathematical modeling of the problem includes equations of motion and continuity. The fluid flow is investigated by converting the equations into a non-dimensionalized form simplified considering long wavelength and low Reynolds number approximation. The analytic expressions for axial velocity, pressure gradient, and pressure rise over a single wavelength cycle are obtained. The impact of various parameters such as slip parameter, viscosity parameter, angle of inclination, gravity parameter and amplitude ratio on axial velocity, pressure gradient and pressure rise are discussed in detail by plotting graphs in MATLAB R2018b software. In this article, a comparison of linear and nonlinear variation of viscosity of bile has been made. It is concluded that velocity and pressure rise is more in case linear variation of viscosity, whereas more pressure gradient is required in case of nonlinear variation of viscosity.

scholarly journals Peristaltic transport of a fractional Burgers’ fluid with variable viscosity through an inclined tube

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Hassan Rachid
Keyword(s):  
Reynolds Number ◽  
Radial Direction ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Mechanical Efficiency ◽  
Peristaltic Transport ◽  
Long Wavelength ◽  
Inclined Tube ◽  
Burgers Fluid

AbstractIn the present study,we investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Burgers’ model in an inclined tube. We suppose that the viscosity is variable in the radial direction. This analysis has been carried out under low Reynolds number and long-wavelength approximations. An analytical solution to the problem is obtained using a fractional calculus approach. Figures are plotted to show the effects of angle of inclination, Reynolds number, Froude number, material constants, fractional parameters, parameter of viscosity and amplitude ratio on the pressure gradient, pressure rise, friction force, axial velocity and on the mechanical efficiency.

scholarly journals Simultaneous Effects of Heat Transfer and Variable Viscosity on Peristaltic Transport of Casson Fluid Flow in an Inclined Porous Tube

2019 ◽  
Vol 24 (2) ◽  
pp. 309-328 ◽  
Author(s):  
G. Manjunatha ◽  
C. Rajashekhar ◽  
H. Vaidya ◽  
K.V. Prasad
Keyword(s):  
Heat Transfer ◽  
Frictional Force ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Darcy Number ◽  
Casson Fluid ◽  
Slip Yield Stress ◽  
Varying Viscosity

Abstract The present study investigates the combined effects of varying viscosity and heat transfer on a Casson fluid through an inclined porous axisymmetric tube in the presence of slip effects. The modeled governing equations are solved analytically by considering the long wavelength and small Reynolds number approximations. The numerical integration is employed to obtain pressure rise and frictional force. A parametric analysis has been presented to study the effects of the Darcy number, angle of inclination, varying viscosity, velocity slip, thermal slip, yield stress, amplitude ratio, Prandtl number and Eckert number on the pressure rise, pressure gradient, streamlines, frictional force and temperature. The study reveals that an increase in the angle of inclination and viscosity parameter has a proportional increase in the pressure rise. Also, an increase in the porosity causes a significant reduction in the pressure rise.

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