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.

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.

Peristaltic transport of a Jeffrey fluid with double-diffusive convection in nanofluids in the presence of inclined magnetic field

2018 ◽  
Vol 15 (11) ◽  
pp. 1850181 ◽  
Author(s):  
Safia Akram ◽  
M. Zafar ◽  
S. Nadeem
Keyword(s):  
Fluid Model ◽  
Concentration Field ◽  
Pressure Rise ◽  
Peristaltic Transport ◽  
Jeffrey Fluid ◽  
Double Diffusive Convection ◽  
Long Wavelength ◽  
Diffusive Convection ◽  
Stream Functions ◽  
Double Diffusive

In this paper, the effects of peristaltic transport with double-diffusive convection in nanofluids through an asymmetric channel with different waveforms is presented. Mathematical modeling for two-dimensional and two-directional flows of a Jeffery fluid model along with double-diffusive convection in nanofluids are given. Exact solutions are obtained for nanoparticle fraction field, concentration field, temperature field, stream functions, pressure gradient and pressure rise in terms of axial and transverse coordinates under the restrictions of long wavelength and low Reynolds number. With the help of computational and graphical results, the effects of Brownian motion, thermospheres, Dufour, Soret and Grashof numbers (thermal, concentration, nanoparticles) on peristaltic flow patterns with double-diffusive convection are discussed.

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 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.

Flow of a Giesekus Fluid in a Planar Channel due to Peristalsis

2013 ◽  
Vol 68 (8-9) ◽  
pp. 515-523 ◽  
Author(s):  
Nasir Ali ◽  
Tariq Javed
Keyword(s):  
Exact Solution ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Longitudinal Velocity ◽  
Pressure Rise ◽  
Nonlinear Ordinary Differential Equation ◽  
Planar Channel ◽  
Long Wavelength ◽  
Dimensional Parameters ◽  
Giesekus Fluid

An attempt is made to investigate the peristaltic motion of a Giesekus fluid in a planar channel under long wavelength and low Reynolds number approximations. Under these assumptions, the flow problem is modelled as a second-order nonlinear ordinary differential equation. Both approximate and exact solution of this equation are presented. The validity of the approximate solution is examined by comparing it with the exact solution. A parametric study is performed to analyze the effects of non-dimensional parameters associated with the Giesekus fluid model (a and We) on flow velocity, pressure rise per wavelength, and trapping phenomenon. It is found that the behaviour of longitudinal velocity and pattern of streamlines for a Giesekus fluid deviate from their counterparts for a Newtonian fluid by changing the parameters a and We. In fact, the magnitude of the longitudinal velocity at the center of the channel for a Giesekus fluid is less than that for a Newtonian fluid. It is also observed that the pressure rise per wavelength decreases in going form Newtonian to Giesekus fluid. Moreover, the size of trapped bolus is large and it circulates faster for a Newtonian fluid in comparison to a Giesekus fluid.

Creeping Flow of Phan-Thien–Tanner Fluids in a Peristaltic Tube With an Infinite Long Wavelength

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Abd El Hakeem Abd El Naby
Keyword(s):  
Friction Force ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Creeping Flow ◽  
Physical Parameters ◽  
Long Wavelength ◽  
Ptt Model ◽  
Peristaltic Pumping ◽  
Parameters Of Interest ◽  
Good Agreement

In this study both linearized and the exponential forms of the Phan-Thien–Tanner model (PTT) are used to simulate the peristaltic flow in a tube. The solutions are investigated under zero Reynolds number and infinitely long wavelength assumptions. Computational solutions are obtained for pressure rise and friction force. The results of the average chyme velocity in the small intestine show that the PTT model is in good agreement with the experimental results, as shown in Table 1. Also, the magnitude of pressure rise and friction force of the exponential PTT model are smaller than in linear PTT model for different values of flow rate. The peristaltic pumping and the augmented pumping are discussed for various values of the physical parameters of interest. The pressure rise and friction force of PTT were compared with other studies in both Newtonian and non-Newtonian cases.

Application of Rabinowitsch Fluid Model in Peristalsis

2014 ◽  
Vol 69 (8-9) ◽  
pp. 473-480 ◽  
Author(s):  
Noreen Sher Akbar ◽  
Sohail Nadeemb
Keyword(s):  
Pressure Gradient ◽  
Wave Motion ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Process Time ◽  
Peristaltic Pumping ◽  
Uniform Tube ◽  
Velocity Pressure

In the present article, we have studied the Rabinowitsch fluid model for the peristaltic flow. The non-Newtonian nature of the fluid is analyzed mathematically by considering the Rabinowitsch fluid. The Rabinowitsch fluid model for the peristaltic flow is not discussed so far. This is the first article describing the features of Rabinowitsch fluid in peristaltic literature. The fluid is flowing in a uniform tube with the wave motion. Exact solutions have been calculated for velocity and pressure gradient. The physical behavior of different parameters for velocity, pressure rise, streamlines, and pressure gradient have been examined graphically. It is observed that when Weissenberg number is large then the relaxation time of the fluid is greater than a specific process time in which the pressure rise increases rapidly in the peristaltic pumping regions. Trapping phenomena have been discussed at the end of the article

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.

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