scholarly journals Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
R. Ellahi ◽  
Arshad Riaz ◽  
S. Nadeem ◽  
M. Ali
Keyword(s):  
Porous Medium ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Nonlinear Partial Differential Equations ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Carreau Fluid ◽  
Highly Nonlinear ◽  
Stream Functions ◽  
Physical Features

We have examined the peristaltic flow of Carreau fluid in a rectangular channel through a porous medium. The governing equations of motion are simplified by applying the long wavelength and low Reynolds number approximations. The reduced highly nonlinear partial differential equations are solved jointly by homotopy perturbation and Eigen function expansion methods. The expression for pressure rise is computed numerically by evaluating the numerical integration. The physical features of pertinent parameters have been discussed by plotting graphs of velocity, pressure rise, pressure gradient, and stream functions.

Mathematical study for peristaltic flow of Williamson fluid in a curved channel

2015 ◽  
Vol 08 (01) ◽  
pp. 1550005 ◽  
Author(s):  
E. N. Maraj ◽  
Noreen Sher Akbar ◽  
S. Nadeem
Keyword(s):  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Curved Channel ◽  
Partial Differential ◽  
Williamson Fluid ◽  
Highly Nonlinear ◽  
Frame Transformation

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

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 MHD Peristaltic Flow of Fractional Jeffrey Model through Porous Medium

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoyi Guo ◽  
Jianwei Zhou ◽  
Huantian Xie ◽  
Ziwu Jiang
Keyword(s):  
Porous Medium ◽  
Pressure Rise ◽  
Maxwell Fluid ◽  
Peristaltic Flow ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Viscoelastic Parameters ◽  
Special Cases ◽  
Generalized Second Grade Fluid

The magnetohydrodynamic (MHD) peristaltic flow of the fractional Jeffrey fluid through porous medium in a nonuniform channel is presented. The fractional calculus is considered in Darcy’s law and the constitutive relationship which included the relaxation and retardation behavior. Under the assumptions of long wavelength and low Reynolds number, the analysis solutions of velocity distribution, pressure gradient, and pressure rise are investigated. The effects of fractional viscoelastic parameters of the generalized Jeffrey fluid on the peristaltic flow and the influence of magnetic field, porous medium, and geometric parameter of the nonuniform channel are presented through graphical illustration. The results of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid, are also deduced as special cases. The comparison among them is presented graphically.

Effects of the wall properties on unsteady peristaltic flow of an Eyring–Powell fluid in a three-dimensional rectangular duct

2015 ◽  
Vol 08 (06) ◽  
pp. 1550081 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Peristaltic Flow ◽  
Solution Technique ◽  
Rectangular Duct ◽  
Governing Equations ◽  
Long Wavelength ◽  
Stream Functions

In the present investigation, peristaltic flow of non-Newtonian fluid model (Eyring–Powell) has been taken into consideration in a cross-section of three-dimensional rectangular channel. The flow is taken to be unsteady and incompressible. The observations are made under the limitations of low Reynolds number and long wavelength which helps in reducing the governing equations. The walls of the channel are supposed to be compliant. The obtained equations are nonlinear partial differential equation of second order and have been solved analytically by using series solution technique. The achieved results are then portrayed graphically to see the variation of various emerging parameters on the profile of velocity. The stream functions have also been sketched in order to discuss the trapping behavior of the circular bolus.

scholarly journals The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. M. Khaled ◽  
Abdelhalim Ebaid ◽  
Fahd Al Mutairi
Keyword(s):  
Pressure Gradient ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Pressure Rise ◽  
Approximate Solutions ◽  
Peristaltic Flow ◽  
Nanoparticle Concentration ◽  
Homotopy Perturbation ◽  
Physical Phenomena ◽  
The Mathematical Model

The problem of the peristaltic flow of a nanofluid under the effect of an endoscope is reinvestigated. The mathematical model is governed by a system of linear and nonlinear partial differential equations with prescribed boundary conditions. Really, the exact solution for any physical problem, if available, is of great importance which inevitably leads to a better understanding of the behaviour of the involved physical phenomena. An attempt for doing so has been done in the present paper, where the temperature equation is solved exactly by the help of Laplace transform and, accordingly, the exact expressions for the nanoparticle concentration, the axial velocity, the pressure gradient, and the pressure rise are established. Furthermore, it is showed in this paper that the physical interpretations of some involved phenomena are found totally different than those previously obtained by the approximate solutions using the homotopy perturbation method. In addition, several comparisons between the current results and the approximate ones have been displayed. Finally, the effect of various parameters on the temperature distribution, the nanoparticle concentration, the pressure gradient, and the pressure rise has been also discussed through graphs.

scholarly journals MHD Effect on Peristaltic Transport for Rabinowitsch Fluid through A Porous Medium in Cilia Channel

2020 ◽  
pp. 1461-1472
Author(s):  
Saba S. Hasen ◽  
Ahmed M. Abdulhadi
Keyword(s):  
Porous Medium ◽  
Hartmann Number ◽  
Perturbation Technique ◽  
Nonlinear Partial Differential Equations ◽  
Reynold Number ◽  
Peristaltic Flow ◽  
Mass Motion ◽  
Governing Equations ◽  
Long Wavelength ◽  
The Magnetic Field

This paper is employed to discuss the effects of the magnetic field and heat transfer on the peristaltic flow of Rabinowitsch fluid through a porous medium in the cilia channel. The governing equations (mass, motion, and energy) are formulated and then the assumptions of long wavelength and low Reynold number are used for simplification. The velocity field, pressure gradient, temperature, and streamlines are obtained when the perturbation technique is applied to solve the nonlinear partial differential equations. The study shows that the velocity is decreased with increasing Hartmann number while it is decreased with increasing the porosity.

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.

scholarly journals Influence of an Inclined Magnetic Field and Rotation on the Peristaltic Flow of a Micropolar Fluid in an Inclined Channel

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Ajaz Ahmad Dar ◽  
K. Elangovan
Keyword(s):  
Magnetic Field ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Volume Flow Rate ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Inclined Magnetic Field ◽  
Symmetric Channel ◽  
Highly Nonlinear

This present article deals with the interaction of both rotation and inclined magnetic field on peristaltic flow of a micropolar fluid in an inclined symmetric channel with sinusoidal waves roving down its walls. The highly nonlinear equations are simplified by adopting low Reynolds number and long wavelength approach. The analytical and numerical solutions for axial velocity, spin velocity, volume flow rate, pressure gradient, pressure rise per wavelength, and stream function have been computed and analyzed. The quantitative effects of various embedded physical parameters are inspected and displayed graphically with fussy prominence. Pressure rise, frictional forces, and pumping phenomenon are portrayed and characterized graphically.

Some Exact Solutions to Equations of Motion of an Incompressible Second Grade Fluid

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Saif Ullah ◽  
Irsa Maqbool
Keyword(s):  
Exact Solutions ◽  
Equations Of Motion ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Complex Functions ◽  
Contour Plots ◽  
Stream Functions ◽  
Grade Fluid ◽  
Steady Plane ◽  
Physical Features

In this paper, we derive some exact solutions of the equations governing the steady plane motions of an incompressible second grade fluid. For this purpose, the vorticity and stream functions both are expressed in terms of complex variables and complex functions. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. Some physical features of the derived solutions are also illustrated by their contour plots.

Series solution of unsteady peristaltic flow of a Carreau fluid in small intestines

2014 ◽  
Vol 07 (05) ◽  
pp. 1450049 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi ◽  
Noreen Sher Akbar
Keyword(s):  
Numerical Integration ◽  
Series Solution ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Frame Of Reference ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Frictional Forces ◽  
Small Intestines ◽  
Uniform Tube

The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the consideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.

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