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 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 Peristaltic flow of a Jeffrey fluid in a rectangular duct having compliant walls

2013 ◽  
Vol 19 (3) ◽  
pp. 399-409 ◽  
Author(s):  
S. Nadeem ◽  
Arshad Riaz ◽  
R. Ellahi
Keyword(s):  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Jeffrey Fluid ◽  
Rectangular Duct ◽  
Mathematical Study ◽  
Three Dimensional Flow ◽  
Long Wavelength ◽  
Compliant Walls ◽  
Parameters Of Interest

In this article, the theoretical and mathematical study of peristaltic transport of a Jeffrey fluid in a rectangular duct with compliant walls is discussed. The constitutive equations are simplified under the implementation of low Reynolds number and long wavelength approximations. The analytical solution of the resulting equations is evaluated by Eigen function expansion method. The graphical aspects of all the parameters of interest are also analyzed. The graphs of velocity for two and three dimensional flow are plotted. The trapping bolus phenomenon is also discussed though streamlines.

THREE-DIMENSIONAL PERISTALTIC FLOW OF A WILLIAMSON FLUID IN A RECTANGULAR CHANNEL HAVING COMPLIANT WALLS

2014 ◽  
Vol 14 (01) ◽  
pp. 1450002 ◽  
Author(s):  
R. ELLAHI ◽  
ARSHAD RIAZ ◽  
S. NADEEM
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Williamson Fluid ◽  
Eigenfunction Expansion Method ◽  
Compliant Walls

In this study, the mathematical observations for the peristaltic flow of a Williamson fluid model (e.g., chyme) in a cross-section of a rectangular duct having compliant walls were considered. The flow was assumed incompressible and unsteady. The constitutive equations were reduced under the assumptions of low Reynolds number and long wavelength approximations. The resulting dimensionless governing equations were solved using the homotopy perturbation method (HPM) and eigenfunction expansion method. The results obtained were explained graphically. The velocity distribution was plotted for physical parameters both in two and three dimensions. The streamline graphs are presented in the end, which explain the trapping bolus phenomenon. All theoretical and graphical results are then discussed simultaneously.

ANALYTICAL AND NUMERICAL SOLUTIONS OF PERISTALTIC FLOW OF WILLIAMSON FLUID MODEL IN AN ENDOSCOPE

2011 ◽  
Vol 11 (04) ◽  
pp. 941-957 ◽  
Author(s):  
NOREEN SHER AKBAR ◽  
S. NADEEM
Keyword(s):  
Numerical Solutions ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Peristaltic Motion ◽  
Governing Equations ◽  
Williamson Fluid ◽  
Long Wavelength ◽  
Good Agreement

The present studies deal with the peristaltic motion of an incompressible Williamson fluid model in an endoscope. The governing equations of Williamson fluid model are first simplify using the assumptions of long wavelength and low Reynolds number. The four types of solutions have been presented for velocity profile named (i) exact solution, (ii) perturbation solution, (iii) HAM solution, and (iv) numerical solutions. The comparisons of four solutions have been found a very good agreement between all the solutions. In addition, the expressions for pressure rise and velocity against various physical parameters are discussed through graphs.

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 Theoretical Study of Heat Transfer on Peristaltic Transport of Non-Newtonian Fluid Flowing in a Channel: Rabinowitsch Fluid Model

2018 ◽  
Vol 3 (4) ◽  
pp. 450-471 ◽  
Author(s):  
U. P. Singh ◽  
Amit Medhavi ◽  
R. S. Gupta ◽  
Siddharth Shankar Bhatt
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Friction Force ◽  
Newtonian Fluid ◽  
Theoretical Study ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Long Wavelength ◽  
Velocity Pressure

The present investigation is concerned with the problem of heat transfer and peristaltic flow of non-Newtonian fluid using Rabinowitsch fluid model through a channel under long wavelength and low Reynolds number approximation. Expressions for velocity, pressure gradient, pressure rise, friction force and temperature have been obtained. The effect of different parameters on velocity, pressure gradient, pressure rise, streamlines, friction force and temperature have been discussed through graphs.

Application of Rabinowitsch Fluid Model for the Mathematical Analysis of Peristaltic Flow in a Curved Channel

2015 ◽  
Vol 70 (7) ◽  
pp. 513-520 ◽  
Author(s):  
Ehnber Naheed Maraj ◽  
Sohail Nadeem
Keyword(s):  
Current Problem ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Shear Stresses ◽  
Curved Channel ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Dimensional Parameters ◽  
Wavelength Approximation

AbstractThe present work is the mathematical investigation of peristaltic flow of Rabinowitsch fluid in a curved channel. The current problem is modeled and solutions for non-dimensional differential equation are obtained under low Reynolds number and long wavelength approximation. The effects of long lasting non-dimensional parameters on exact solution for velocity profile, pressure rise and shear stresses are studied graphically in the last section. Tables are also incorporated for shear stresses at the walls of the curved channel.

scholarly journals Effect of Lateral Walls on Peristaltic Flow through an Asymmetric Rectangular Duct

2011 ◽  
Vol 8 (3-4) ◽  
pp. 295-308 ◽  
Author(s):  
Kh. S. Mekheimer ◽  
S. Z.-A. Husseny ◽  
A. I. Abd el Lateef
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Viscous Fluid ◽  
Wave Train ◽  
Peristaltic Flow ◽  
Frame Of Reference ◽  
Rectangular Duct ◽  
Long Wavelength ◽  
Flow Through ◽  
Lateral Walls

Peristaltic transport of an incompressible viscous fluid due to an asymmetric waves propagating on the horizontal sidewalls of a rectangular duct is studied under long-wavelength and low-Reynolds number assumptions. The peristaltic wave train on the walls have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effect of aspect ratio, phase difference, varying channel width and wave amplitudes on the pumping characteristics and trapping phenomena are discussed in detail. The results are compared to with those corresponding to Poiseuille flow.

A mixed finite element/control volume model of wind-driven circulation in lakes

2013 ◽  
Vol 5 (1) ◽  
Author(s):  
Victor Podsechin
Keyword(s):  
Control Volume ◽  
Mixed Finite Element ◽  
Surface Wind ◽  
Three Dimensional ◽  
Circulation Model ◽  
Hydrodynamic Equations ◽  
Governing Equations ◽  
Near Surface ◽  
Stream Functions ◽  
Surface Wind Field

AbstractA three-dimensional numerical circulation model is described. The model is based on non-linear hydrodynamic equations, modified according to hydrostatic and Boussinesq approximations. A space-splitting scheme is used for numerical approximations of governing equations. The simple hypothesis on elliptic stream functions shape is utilized to reconstruct the near-surface wind field. The calculated currents correspond reasonably well with observed velocities in different locations lake-wide.

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