Analytic Approximate Solutions and Numerical Results for Stagnation Point Flow of Jeffrey Fluid Towards an Off-Centered Rotating Disk

2014 ◽  
Vol 31 (2) ◽  
pp. 201-215 ◽  
Author(s):  
N. A. Khan ◽  
S. Khan ◽  
F. Riaz
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Approximate Solutions ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case ◽  
Non Linear Equations

AbstractThe present paper studies the three-dimensional, off centered stagnation flow of a Jeffrey fluid over a rotating disk. The governing non-linear equations and their associated boundary conditions are transformed into coupled ordinary differential equations by utilizing an appropriate similarity transformation. Homotopy analysis method is utilized to evaluate the analytical solution in the form of infinite series. Also, the convergence region of the obtained solution is determined and plotted. The effects of pertaining parameters on radial, azimuthal and induced velocities of the fluid flow are presented graphically and discussed. Moreover comparisons have also been made with the previous results as a special case.

scholarly journals Off-Centered Stagnation Point Flow of a Couple Stress Fluid towards a Rotating Disk

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Similarity Transformation ◽  
Rotating Disk ◽  
Analytical Approximation ◽  
Couple Stress Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case

An investigation has been made to study the off-centered stagnation flow of a couple stress fluid over a rotating disk. The model developed for the governing problem in the form of partial differential equations has been converted to ordinary differential equations with the use of suitable similarity transformation. The analytical approximation has been made with the most promising analytical approach, homotopy analysis method (HAM). The convergence region of the obtained solution is determined and plotted. The effects of couple stress and nondimensional parameters have been observed on the flows of couple stress fluid. Also comparison has been made with the Newtonian fluid as the special case of considered problem.

scholarly journals Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Sohrab Effati ◽  
Hassan Saberi Nik ◽  
Reza Buzhabadi
Keyword(s):  
Homotopy Analysis Method ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Reaction Diffusion Equations ◽  
Analysis Method ◽  
Coupled Equations ◽  
Homotopy Analysis ◽  
Special Case

The homotopy analysis method (HAM) is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The efficiency and accuracy of the method are verified by using two famous examples: coupled Burgers and mKdV equations. The obtained results show that the homotopy perturbation method is a special case of homotopy analysis method.

Analytic Solution for the Magnetohydrodynamic Rotating Flow of Jeffrey Fluid in a Channel

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Asghar ◽  
Awatif A. Hendi
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Rotating System ◽  
Electrically Conducting ◽  
Similarity Transformations ◽  
Homotopy Analysis

In this work, the homotopy analysis method is applied to enable discussion of the three-dimensional shrinking flow of Jeffrey fluid in a rotating system. The fluid is electrically conducting in the presence of a uniform applied magnetic field, and the induced magnetic field is neglected. The similarity transformations reduce the nonlinear partial differential equations into ordinary differential equations. The convergence of the obtained solutions is checked. Graphs are plotted and discussed for various parameters of interest.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

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