Series Solutions for the Peristaltic Flow of a Tangent Hyperbolic Fluid in a Uniform Inclined Tube

2010 ◽  
Vol 65 (11) ◽  
pp. 887-895 ◽  
Author(s):  
Sohail Nadeem ◽  
Noreen Sher Akbar
Keyword(s):  
Amplitude Ratio ◽  
Pressure Rise ◽  
Reynold Number ◽  
Weissenberg Number ◽  
Long Wavelength ◽  
Inclined Tube ◽  
Homotopy Analysis ◽  
Tangent Hyperbolic Fluid ◽  
Power Law Index ◽  
Good Agreement

In the present investigation we have studied a tangent hyperbolic fluid in a uniform inclined tube. The governing equations are simplified using long wavelength and low Reynold number approximations. The solutions of the problem in simplified form are calculated with two methods namely (i) the perturbation method and (ii) the homotopy analysis method. The comparison of the solutions show a very good agreement between the two results. At the end of the article the expressions of the pressure rise and the frictional force are calculated with the help of numerical integration. The graphical results are presented to show the physical behaviour of Weissenberg number We, amplitude ratio φ , and tangent hyperbolic power law index n.

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 Peristaltic viscoelastic fluid motion in a tube

2001 ◽  
Vol 26 (1) ◽  
pp. 21-34 ◽  
Author(s):  
Elsayed F. Elshehawey ◽  
Ayman M. F. Sobh
Keyword(s):  
Amplitude Ratio ◽  
Fluid Motion ◽  
Perturbation Expansion ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Wave Number ◽  
Physical Parameters ◽  
Oldroyd Fluid ◽  
Pumping Rate ◽  
Axisymmetric Tube

Peristaltic motion of viscoelastic incompressible fluid in an axisymmetric tube with a sinusoidal wave is studied theoretically in the case that the radius of the tube is small relative to the wavelength. Oldroyd flow has been considered in this study and the problem is formulated and analyzed using a perturbation expansion in terms of the variation of the wave number. This analysis can model the chyme movement in the small intestine by considering the chyme as an Oldroyd fluid. We found out that the pumping rate of Oldroyd fluid is less than that for a Newtonian fluid. Further, the effects of Reynolds number, Weissenberg number, amplitude ratio and wave number on the pressure rise and friction force have been discussed. It is found that the pressure rise does not depend on Weissenberg number at a certain value of flow rate. The results are studied for various values of the physical parameters of interest.

Influence of metachronal wave on hyperbolic tangent fluid model with inclined magnetic field

2019 ◽  
Vol 16 (09) ◽  
pp. 1950139 ◽  
Author(s):  
Safia Akram ◽  
Farkhanda Afzal ◽  
Muhammad Imran
Keyword(s):  
Newtonian Fluid ◽  
Fluid Model ◽  
Perturbation Technique ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Hyperbolic Tangent ◽  
Regular Perturbation ◽  
Tangent Hyperbolic Fluid ◽  
Wavelength Approximation ◽  
Induced Flow

The purpose of this paper is to discuss the theoretical study of a nonlinear problem of cilia induced flow by considering the fluid as anincompressible non-Newtonian fluid (hyperbolic tangent fluid) model by means of ciliated walls. The leading equations of present flow problem are simplified under the consideration of long-wavelength approximation. We have utilized regular perturbation technique to solve the simplified leading equations of hyperbolic tangent fluid model. The analytical solution is computed for stream function and numerical solution is computed for the rise in pressure. The characteristics of the ciliary system on tangent hyperbolic fluid are analyzed graphically and discussed in detail. It has been found that when [Formula: see text], the results of pressure rise coincide with the results of Newtonian fluid. It has also been observed that the size of the trapping bolus decreases with an increase in Hartmann number and Weissenberg number.

scholarly journals Transfer of heat and hall current effects on peristaltic flow of a bingham fluid in a channel by Adomian decomposition method

2021 ◽  
Vol 9 (3) ◽  
pp. 250-259
Keyword(s):  
Frictional Force ◽  
Hall Current ◽  
Amplitude Ratio ◽  
Pressure Rise ◽  
Adomian Decomposition Method ◽  
Darcy Number ◽  
Bingham Fluid ◽  
Peristaltic Flow ◽  
Long Wavelength ◽  
Adomian Decomposition

This paper concerns with the transfer of heat and hall current effects on peristaltic flow of a Bingham fluid in a channel is analysis. Resulting differential equations after implementation of small Reynolds number and long wavelength considerations are numerically solved. The expressions for different parameters like pressure rise, flow rate and frictional force are determined. The effect of magnetic field, Darcy number, yield stress, amplitude ratio, Hall parameter and the temperature on pressure gradient, pumping characteristics and frictional force are discussed through nature of graphs

Unsteady Flow of Magneto Thermomicropolar Fluid in a Porous Channel With Peristalsis: Unsteady Separation

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Y. Abd Elmaboud
Keyword(s):  
Unsteady Flow ◽  
Amplitude Ratio ◽  
Flow Behavior ◽  
Fluid Velocity ◽  
Flow Analysis ◽  
Pressure Rise ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Unsteady Separation ◽  
Raphson Method

The magneto thermodynamic aspects of micropolar fluid (blood model) through an isotropic porous medium in a nonuniform channel with rhythmically contracting walls have been investigated. The flow analysis has been discussed under long wavelength and low Reynolds number approximations. The closed form solutions are obtained for velocity components, microrotation, heat transfer, as well as the wall vorticity. The modified Newton–Raphson method is used to predict the unsteady flow separation points along the peristaltic wall. Numerical computations have been carried out for the pressure rise per wavelength. The study shows that peristaltic transport, fluid velocity, microrotation velocity, and wall shear stress are significantly affected by the nonuniform geometry of the blood vessels. Moreover, the amplitude ratio, the coupling number, the micropolar parameter, and the magnetic parameter are important parameters that affect the flow behavior.

Effects of Heat Transfer on Peristaltic Transport of a Bingham Fluid through an Inclined Tube with Different Wave Forms

2019 ◽  
Vol 392 ◽  
pp. 158-177 ◽  
Author(s):  
Hanumesh Vaidya ◽  
Choudhari Rajashekhar ◽  
Gudekote Manjunatha ◽  
K.V. Prasad
Keyword(s):  
Heat Transfer ◽  
Plug Flow ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Bingham Fluid ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Inclined Tube ◽  
Wave Forms ◽  
Velocity Pressure

The present study investigates the effects of slip and heat transfer on peristaltic mechanism of Bingham fluid in an inclined tube. The sinusoidal, multi-sinusoidal, triangular, square and trapezoidal wave forms are considered. The analysis has been carried out under the assumptions of long wavelength and small Reynold's number approximations. The closed-form solutions are obtained for velocity, plug flow velocity, pressure gradient, streamlines, and temperature. The numerical integration is employed to investigate the effects of pressure rise and frictional force. The influence of relevant parameters on physiological quantities of interest is analyzed and discussed through graphs. The study reveals that velocity and thermal slip have a decreasing effect on velocity and temperature. Further, it is noticed that the volume of trapped bolus increases for increasing values of velocity slip parameter.

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.

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.

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.

scholarly journals Peristaltic Motion of Carreau Fluid in a Channel with Convective Boundary Conditions

2014 ◽  
Vol 11 (3) ◽  
pp. 157-168 ◽  
Author(s):  
T. Hayat ◽  
Humaira Yasmin ◽  
A. Alsaedi
Keyword(s):  
Boundary Conditions ◽  
Mathematical Formulation ◽  
Pressure Rise ◽  
Weissenberg Number ◽  
Convective Boundary Conditions ◽  
Peristaltic Motion ◽  
Carreau Fluid ◽  
Convective Boundary ◽  
Long Wavelength ◽  
Axial Pressure Gradient

We investigate the peristaltic motion of Carreau fluid in an asymmetric channel with convective boundary conditions. Mathematical formulation is first reduced in a wave frame of reference and then solutions are constructed by long wavelength and low Reynolds number conventions. Results of the stream function, axial pressure gradient, temperature and pressure rise over a wavelength are obtained for small Weissenberg number. Velocity and temperature distributions are analyzed for different parameters of interest. A comparative study between the results of Newtonian and Carreau fluids is given.

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