ON ACCELERATED FLOWS OF MAGNETOHYDRODYNAMIC THIRD GRADE FLUID IN A POROUS MEDIUM AND ROTATING FRAME VIA A HOMOTOPY ANALYSIS METHOD

2014 ◽  
Vol 17 (11) ◽  
pp. 969-981
Author(s):  
Mojtaba Nazari ◽  
Zainal Abdul Aziz ◽  
Faisal Salah
Keyword(s):  
Porous Medium ◽  
Homotopy Analysis Method ◽  
Third Grade ◽  
Rotating Frame ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid

scholarly journals Constant Accelerated Flow for a Third-Grade Fluid in a Porous Medium and a Rotating Frame with the Homotopy Analysis Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zainal Abdul Aziz ◽  
Mojtaba Nazari ◽  
Faisal Salah ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Porous Medium ◽  
Analytic Solution ◽  
Third Grade ◽  
Approximate Analytic Solution ◽  
Rotating Frame ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Accelerated Flow

The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of a constant accelerated flow for a third-grade fluid in a porous medium and a rotating frame. HAM is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. The approximate analytic solution for constant accelerated flow is obtained by using HAM. HAM contains the auxiliary parameterℏ, which provides us with a straightforward way to obtain the convergence region of the series solution. Graphical results are plotted and the consequences discussed. The obtained solutions clearly satisfy the governing equations and all the imposed initial and boundary conditions. Many interesting results can be obtained as the special cases of the presented analysis. The influence of the material parameters of a third-grade fluid and rotation upon the velocity field is finally deliberated.

Numerical Results of a Flow in a Third Grade Fluid between Two Porous Walls

2009 ◽  
Vol 64 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Tasawar Hayat ◽  
Rahmat Ellahi ◽  
Saleem Asghar
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Material Parameter ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Porous Walls

Series solution for a steady flow of a third grade fluid between two porous walls is given by the homotopy analysis method (HAM). Comparison with the existing numerical solution is shown. It is found that, unlike the numerical solution, the present series solution holds for all values of the material parameter of a third grade fluid.

Unsteady Flow of Third Grade Fluid With Soret and Dufour Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Asghar ◽  
S. Obaidat
Keyword(s):  
Unsteady Flow ◽  
Temperature Fields ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Soret And Dufour Effects ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Homotopy Analysis ◽  
Grade Fluid

Unsteady flow of a third grade fluid in the presence of Soret and Dufour effects is considered. Employing similarity transformations, the governing equation for the velocity, concentration, and temperature fields is presented. The computations for the corresponding problems are performed by using a homotopy analysis method (HAM). The associated behavior of the flow parameters is discussed and important conclusions have been pointed out.

scholarly journals A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
R. Ellahi
Keyword(s):  
Homotopy Analysis Method ◽  
Variable Viscosity ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Series Solutions ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Physical Features

This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method (HAM) is employed for the presentation of series solutions. The HAM is accepted as an elegant tool for effective solutions for complicated nonlinear problems. The solutions of (Hayat et al., 2007) are developed, and their convergence has been discussed explicitly for two different models, namely, constant and variable viscosity. An error analysis is also described. In addition, the obtained results are illustrated graphically to depict the convergence region. The physical features of the pertinent parameters are presented in the form of numerical tables.

scholarly journals COUETTE FLOW PROBLEM FOR AN UNSTEADY MHD THIRD-GRADE FLUID WITH HALL CURRENTS

2014 ◽  
Vol 15 (2) ◽  
Author(s):  
Muhammad Azram ◽  
Haider Zaman
Keyword(s):  
Linear Problem ◽  
Flow Problem ◽  
Hartmann Number ◽  
Hall Current ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Hall Parameter ◽  
Homotopy Analysis ◽  
Grade Fluid

ABSTRACT: In this work, we analyze Coutte flow problem for an unsteady mangneto-hydrodynamic (MHD) third-grade fluid in the presence of a pressure gradient and Hall currnts. Existing literature on the topic shows that the effecs of Hall current on Coutte flow of an unsteady MHD third-grade fluid with a prssure gradient has not yet been investigated. The arising non-linear problem is solved by the homotopy analysis method (HAM) and the convergence of the obtained complex series solution is carefully analyzed. The effects of pressure number, Hartmann number and Hall parameter on unsteady velocity are discussed via analysis of plots. ABSTRAK: Kajian dijalan untuk menganalisa masalah aliran Coutte bagi bendalir MHD gred ketiga dan arus Hall. Bagi topik ini kesan arus Hall terhadap aliran Couette dalam bendalir MHD gred ketiga tak mantap dengan kecerunan tekanan, belum pernah dikaji selidik.  Masalah tak linear berbangkit diselesaikan dengan kaedah analisis homotopi (HAM) dan ketumpuan solusi rangkaian kompleks dianalisa dengan teliti. Kesan nilai tekanan, nombor Hartmann dan parameter Hall terhadap halaju tak mantap diperbincangkan melalui plot yang dianalisis.KEYWORDS: Cuette; flow; hall currents; unsteady; third-grade fluid; HAM 

A Note on Oscillatory Flow of a Third Grade Fluid in a Porous Medium

2008 ◽  
Vol 11 (5) ◽  
pp. 467-473
Author(s):  
Tasawar Hayat ◽  
F. Shahzad ◽  
S. Asghar
Keyword(s):  
Porous Medium ◽  
Oscillatory Flow ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid
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