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.

Metachronal Wave of Cilia Transport in a Curved Channel

2015 ◽  
Vol 70 (1) ◽  
pp. 33-38 ◽  
Author(s):  
Sohail Nadeem ◽  
Hina Sadaf
Keyword(s):  
Viscous Fluid ◽  
Pressure Rise ◽  
Viscous Effects ◽  
Curved Channel ◽  
Long Wavelength ◽  
Metachronal Wave ◽  
Long Wavelength Approximation ◽  
Two Dimensional Flow ◽  
Wavelength Approximation ◽  
Induced Flow

AbstractIn this article, the mechanism of cilia-induced flow is discussed through a mathematical model. In this analysis two-dimensional flow of a viscous fluid is observed in a curved channel with ciliated walls. The features of ciliary structures are determined by the dominance of viscous effects over inertial effects using the long-wavelength approximation. The flow is modeled in both fixed and wave frame references. The exact solution is calculated for the velocity profile and the flow properties for the viscous fluid are determined as a function of the cilia and metachronal wave velocity. Results for the pressure rise, pressure gradient and stream function are constructed and analyzed graphically.

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.

Slip and Heat Transfer Effects on Peristaltic Motion of a Carreau Fluid in an Asymmetric Channel

2010 ◽  
Vol 65 (12) ◽  
pp. 1121-1127 ◽  
Author(s):  
Tasawar Hayat ◽  
Najma Saleem ◽  
Awatif A. Hendi
Keyword(s):  
Heat Transfer ◽  
Peristaltic Flow ◽  
Asymmetric Channel ◽  
Peristaltic Motion ◽  
Carreau Fluid ◽  
Long Wavelength ◽  
Flow And Heat Transfer ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Pumping And Trapping

An analysis has been carried out for peristaltic flow and heat transfer of a Carreau fluid in an asymmetric channel with slip effect. The governing problem is solved under long wavelength approximation. The variations of pertinent dimensionless parameters on temperature are discussed. Pumping and trapping phenomena are studied.

scholarly journals Effects of Heat and Mass Transfer on MHD Peristaltic Flow of a Non-Newtonian Fluid through a Porous Medium between Two Coaxial Cylinders

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Abeer A. Shaaban ◽  
Mohamed Y. Abou-zeid
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Flow Characteristics ◽  
Fluid Flows ◽  
Peristaltic Flow ◽  
Governing Equations ◽  
Long Wavelength ◽  
Finite Difference Technique ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation

We investigated the influence of heat and mass transfer on the peristaltic flow of magnetohydrodynamic Eyring-Powell fluid under low Reynolds number and long-wavelength approximation. The fluid flows between two infinite cylinders; the inner tube is uniform, rigid, and rest, while the outer flexible tube has a sinusoidal wave traveling down its wall. The governing equations are solved numerically using finite-difference technique. The velocity, temperature, and concentration distribution are obtained. The features of flow characteristics are analyzed by plotting graphs and discussed in detail.

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.

Magnetohydrodynamic Peristaltic Flow of a Pseudoplastic Fluid in a Curved Channel

2013 ◽  
Vol 68 (5) ◽  
pp. 380-390 ◽  
Author(s):  
Saima Noreen ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Magnetic Field ◽  
Series Solution ◽  
Magnetic Force ◽  
Fluid Model ◽  
Peristaltic Flow ◽  
Frame Of Reference ◽  
Induced Magnetic Field ◽  
Curved Channel ◽  
Pseudoplastic Fluid ◽  
Long Wavelength

A mathematical model is developed to examine the effects of an induced magnetic field on the peristaltic flow in a curved channel. The non-Newtonian pseudoplastic fluid model is used to depict the combined elastic and viscous properties. The analysis has been carried out in the wave frame of reference, long wavelength and low Reynolds scheme are implemented. A series solution is obtained through perturbation analysis. Results for stream function, pressure gradient, magnetic force function, induced magnetic field, and current density are constructed. The effects of significant parameters on the flow quantities are sketched and discussed.

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.

scholarly journals Peristaltic Transport of a Particle–Fluid Suspension through a Uniform and Non-Uniform Annulus

2008 ◽  
Vol 5 (2) ◽  
pp. 47-57 ◽  
Author(s):  
K. S. Mekheimer ◽  
Y. Abd Elmaboud
Keyword(s):  
Amplitude Ratio ◽  
Pressure Rise ◽  
Fluid Phase ◽  
Spherical Particles ◽  
Physical Parameters ◽  
Pressure Gradients ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Uniform Tube

This study looks at the influence of an endoscope on the peristaltic flow of a particle–fluid suspension (as blood model) through tubes. A long wavelength approximation through a uniform and non-uniform infinite annulus filled with an incompressible viscous and Newtonian fluid mixed with rigid spherical particles of identical size is investigated theoretically. The inner tube is uniform, rigid and moving with a constant velocity V0, whereas the outer non-uniform tube has a sinusoidal wave travelling down its wall. The axial velocity of the fluid phase uf, particulate phase upand the pressure gradients have been obtained in terms of the dimensionless flow rateQ, the amplitude ratioɸ, particle concentrationC, the velocity constant V0and the radius ratio ϵ (the ratio between the radius of the inner tube and the radius of the outer one at the inlet). Numerical calculations for various values of the physical parameters of interest are carried out for the pressure rise and the friction force on the inner and the outer tubes.

Convective heat transfer analysis for MHD peristaltic flow in an asymmetric channel

2014 ◽  
Vol 07 (03) ◽  
pp. 1450023 ◽  
Author(s):  
M. Awais ◽  
S. Farooq ◽  
H. Yasmin ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Peristaltic Flow ◽  
Heat Transfer Analysis ◽  
Asymmetric Channel ◽  
Convective Conditions ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Wave Trains ◽  
Temperature And Pressure ◽  
The Impact

Magnetohydrodynamic peristaltic flow of Jeffery fluid in an asymmetric channel is addressed. The channel walls satisfy the convective conditions. Asymmetry here is considered due to wave trains of different amplitudes and phases. Solutions for the velocity, temperature and pressure gradient are obtained using long wavelength approximation. Plots reflecting the impact of various parameters of interest are shown and examined.

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