Peristaltic Flow of a Carreau Fluid in a Rectangular Duct

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
S. Nadeem ◽  
Safia Akram ◽  
T. Hayat ◽  
Awatif A. Hendi
Keyword(s):  
Homotopy Perturbation Method ◽  
Wave Length ◽  
Peristaltic Flow ◽  
Rectangular Duct ◽  
Carreau Fluid ◽  
Fixed Frame ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Side Walls ◽  
Horizontal Side

In the present investigation we have studied the peristaltic flow of a Carreau fluid in a rectangular duct. The flow is investigated in the wave frame of reference moving with the velocity c away from the fixed frame. The peristaltic wave propagating on the horizontal side walls of a rectangular duct is studied under long wave length and low Reynolds number approximation. The analytical solutions of velocity and pressure gradient have been found under lubrication approach with the help of Homotopy perturbation method. Graphical results are displayed to see the behavior of various emerging parameters of Carreau fluid. The comparison of the present work is also made with the existing literature.

scholarly journals Analysis of Heating Effects and Different Wave Forms on Peristaltic Flow of Carreau Fluid in Rectangular Duct

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Safia Akram ◽  
Najma Saleem
Keyword(s):  
Peristaltic Transport ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Carreau Fluid ◽  
Heating Effects ◽  
Wave Forms ◽  
Side Walls ◽  
Horizontal Side ◽  
Power Law Index ◽  
The Impact

The existing analysis deals with heat transfer occurrence on peristaltic transport of a Carreau fluid in a rectangular duct. Flow is scrutinized in a wave frame of reference moving with velocity c away from a fixed frame. A peristaltic wave propagating on the horizontal side walls of a rectangular duct is discussed under lubrication approximation. In order to carry out the analytical solution of velocity, temperature, and pressure gradient, the homotopy perturbation method is employed. Graphical results are displayed to see the impact of various emerging parameters of the Carreau fluid and power law index. Trapping effects of peristaltic transport is also discussed and observed that number of trapping bolus decreases with an increase in aspect ratio β.

scholarly journals Homotopy perturbation method to MHD non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis

2017 ◽  
Vol 21 (5) ◽  
pp. 2069-2080 ◽  
Author(s):  
Mohamed Abou-Zeid
Keyword(s):  
Porous Medium ◽  
Axial Velocity ◽  
Homotopy Perturbation Method ◽  
Wave Length ◽  
Nanofluid Flow ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Flow Through ◽  
Eccentric Annuli ◽  
Fundamental Equations

In this contribution, the magnetohydrodynamic non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis is investigated. This has been done under the combined effect of viscous dissipation and radiation. The inner annulus is rigid and at rest, while the outer annulus has a sinusoidal wave traveling down its wall. The fundamental equations are modulated under the long wave length assumptions, and a closed form of solution is obtained for the axial velocity. While, homotopy perturbation solution is obtained, which satisfies the energy and nanoparticles equations. Numerical results for the axial velocity, temperature, and nanoparticles phenomena distributions as well as the reduced Nusselt and Sherwood numbers are obtained and tabulated for various parametric conditions.

Exact Analytical Solution for the Peristaltic Flow of Nanofluids in an Asymmetric Channel with Slip Effect of the Velocity, Temperature and Concentration

2014 ◽  
Vol 30 (4) ◽  
pp. 411-422 ◽  
Author(s):  
E. H. Aly ◽  
A. Ebaid
Keyword(s):  
Brownian Motion ◽  
Temperature Distribution ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Rise Velocity ◽  
Nanoparticle Concentration ◽  
Homotopy Perturbation

AbstractThe peristaltic flow of nanofluids under the effect of slip conditions was theoretically investigated. The mathematical model was governed by a system of linear and non-linear partial differential equations with prescribed boundary conditions. Then, the exact solutions were successfully obtained and reported for the first time in the present work. These exact solutions were then used for studying the effects of the slip, thermophoresis, Brownian motion parameters and many others on the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and pressure gradient. In addition, it is proved that the obtained exact solutions are reduced to the literature results in the special cases.In the general case, it was found that on comparing the current solutions with the approximate ones obtained using the homotopy perturbation method in literature, remarkable differences have been detected for behaviour of the pressure rise, velocity profiles, temperature distribution, nanoparticle concentration and finally the pressure gradient. An example of these differences is about effect of the Brownian motion parameter on the velocity profile; where it was shown in this paper that the small values of this parameter have not a significant effect on the velocity, while this situation was completely different in the published work. Many other significant differences have been also discussed. Therefore, these observed differences recommend the necessity of including the convergence issue when applying the homotopy perturbation method or any other series solution method to solve a physical model. In conclusion. The current results may be considered as a base for any future analysis and/or comparisons.

Short and Long Wave Peristaltic Flow: Modeling and Mathematical Analysis

2015 ◽  
Vol 07 (01) ◽  
pp. 1550014 ◽  
Author(s):  
Lorenzo Fusi ◽  
Angiolo Farina ◽  
Antonio Fasano
Keyword(s):  
Mathematical Model ◽  
Wave Length ◽  
Oscillation Amplitude ◽  
Short Wave ◽  
Peristaltic Flow ◽  
Flow Modeling ◽  
Small Aspect Ratio ◽  
Long Wave ◽  
Short Wave Length ◽  
Axisymmetric Channel

In this paper, we present a mathematical model for the peristaltic flow of a Newtonian fluid in an axisymmetric channel with small aspect ratio. In particular, we study the effects of the wave length of the wall oscillation distinguishing between long wave length (same order of the vessel's length) and short wave length (same order of the vessel's radius). We prove that the oscillation produces flow even in the absence of a pressure gradient in case of long wave. In case of short wave length, peristalsis does not affect the flow. We also prove that, in both cases, the tube resistance increases as the oscillation amplitude increases.

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.

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