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.

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.

scholarly journals Effect of the Velocity Second Slip Boundary Condition on the Peristaltic Flow of Nanofluids in an Asymmetric Channel: Exact Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Emad H. Aly ◽  
Abdelhalim Ebaid
Keyword(s):  
Boundary Condition ◽  
Temperature Distribution ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Slip Boundary Condition ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Nanoparticle Concentration ◽  
Slip Boundary

The problem of peristaltic nanofluid flow in an asymmetric channel in the presence of the second-order slip boundary condition was investigated in this paper. To the best of the authors’ knowledge, this parameter was here incorporated for the first time in such field of a peristaltic flow. The system governing the current flow was found as a set of nonlinear partial differential equations in the stream function, pressure gradient, nanoparticle concentration, and temperature distribution. Therefore, this system has been successfully solved exactly via a very effective procedure. These exact solutions were then proved to reduce to well-known results in the absence of second slip which were published very recently in the literature. Effect of the second slip parameter on the present physical parameters was discussed through graphs and it was found that this type of slip is a very important one to predict the investigated physical model. Moreover, the variation of many physical parameters such as amplitudes of the lower and upper waves, phase difference on the temperature distribution, nanoparticle concentration, pressure rise, velocity, and pressure gradient were also discussed. Finally, the present results may be viewed as an optimal choice for their dependence on the exact solutions which are obtained due to the highly complex nonlinear system.

Influence of an inclined magnetic field on heat and mass transfer of the peristaltic flow of a couple stress fluid in an inclined channel

2017 ◽  
Vol 14 (1) ◽  
pp. 7-18 ◽  
Author(s):  
Ajaz Ahmad Dar ◽  
K. Elangovan
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Pressure Gradient ◽  
Couple Stress ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Inclined Magnetic Field ◽  
Content Type ◽  
Inclined Channel ◽  
Velocity Pressure

Purpose This paper aims to intend for investigating the influence of an inclined magnetic field on the peristaltic flow of a couple stress fluid through an inclined channel with heat and mass transfer. Design/methodology/approach Long wavelength and low Reynolds number methodology is actualized for simplifying the highly nonlinear equations. Mathematical expressions of axial velocity, pressure gradient and volume flow rate are obtained. Pressure rise, frictional force and pumping phenomenon are portrayed and symbolized graphically. Exact and numerical solutions have been carried out. The computed results are presented graphically for various embedded parameters. Temperature and concentration profile are also scrutinized and sketched. Findings Results from the current study concluded that the fluid motion can be enhanced by increasing the inclination of both the magnetic field and the channel. Originality/value The elemental characteristics of this analysis is a complete interpretation of the influence of couple stress parameter and inclination of magnetic field on the velocity, pressure gradient, pressure rise and frictional forces.

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.

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

COMPUTATIONAL SOLUTION OF TEMPERATURE DISTRIBUTION IN A THIN ROD OVER A GIVEN INTERVAL I={x├|0

2021 ◽  
Vol 5 (1) ◽  
pp. 608-618
Author(s):  
Falade Kazeen Iyanda ◽  
Ismail Baoku ◽  
Gwanda Yusuf Ibrahim
Keyword(s):  
Temperature Distribution ◽  
Homotopy Perturbation Method ◽  
Initial Temperature ◽  
Applied Mathematics ◽  
Numerical Algorithms ◽  
Initial Temperature Distribution ◽  
Related Field ◽  
Homotopy Perturbation ◽  
Numerical Tools ◽  
New Iterative Method

In this paper, two analytical–numerical algorithms are formulated based on homotopy perturbation method and new iterative method to obtain numerical solution for temperature distribution in a thin rod over a given finite interval. The effects of different parameters such as the coefficient  which accounts for the heat loss and the diffusivity constant  are examined when initial temperature distribution  (trigonometry and algebraic functions) are considered. The error in both algorithms approaches to zero as the computational length  increases. The proposed algorithms have been demonstrated to be quite flexible, robust and accurate. Thus, the algorithms are established as good numerical tools to solve several problems in applied mathematics and other related field of sciences

The Homotopy-Perturbation Method for Solving Klein-Gordon-Type Equations with Unbounded Right- Hand Side

2009 ◽  
Vol 64 (1-2) ◽  
pp. 149-152 ◽  
Author(s):  
Afgan Aslanov
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Homotopy Perturbation ◽  
Right Hand ◽  
Klein Gordon ◽  
New Type ◽  
Solvable Problems

The approximate and/or exact solutions of the generalized Klein-Gordon- and sine-Gordon-type equations are obtained. We introduce a new type of initial conditions to extend the class of solvable problems

ANTI-BACTERIAL APPLICATIONS FOR NEW THERMAL CONDUCTIVITY MODEL IN ARTERIES WITH CNT SUSPENDED NANOFLUID

2016 ◽  
Vol 16 (05) ◽  
pp. 1650063 ◽  
Author(s):  
NOREEN SHER AKBAR ◽  
M. RAZA ◽  
R. ELLAHI
Keyword(s):  
Magnetic Field ◽  
Pressure Gradient ◽  
Mathematical Formulation ◽  
Pressure Rise ◽  
Darcy Number ◽  
Peristaltic Flow ◽  
Permeable Walls ◽  
Thermal Conductivity Model ◽  
Number Formula ◽  
Physical Quantities

The peristaltic flow of a carbon nanotubes (CNTs) water fluid investigate the effects of heat generation and magnetic field in permeable vertical diverging tube is studied. The mathematical formulation is presented, the resulting equations are solved exactly. The obtained expressions for pressure gradient, pressure rise, temperature, velocity profile are described through graphs for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon. It is observed that pressure gradient profile is decreasing by increase of Darcy number [Formula: see text] because Darcy number is due to porous permeable walls of the tube and when walls are porous fluid cannot easily flow in tube, so that will decrease the pressure gradient.

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