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.

Unsteady Three-Dimensional Flow in a Second-Grade Fluid Over a Stretching Surface

2011 ◽  
Vol 66 (10-11) ◽  
pp. 635-642 ◽  
Author(s):  
Tasawar Hayat ◽  
Ambreen Safdar ◽  
Muhammad Awais ◽  
Awatif A. Hendi
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Second Grade ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Stretching Surface ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Grade Fluid

The three-dimensional unsteady flow induced in a second-grade fluid over a stretching surface has been investigated. Nonlinear partial differential equations are reduced into a system of ordinary differential equations by using the similarity transformations. The homotopy analysis method (HAM) has been implemented for the series solutions. Graphs are displayed for the effects of different parameters on the velocity field.

Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer Over a Stretching Flat Surface by Homotopy Analysis Method

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Ahmer Mehmood ◽  
Asif Ali
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Porous Plate ◽  
Three Dimensional ◽  
Parallel Plates ◽  
Analysis Method ◽  
Electrically Conducting ◽  
Homotopy Analysis

In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

scholarly journals Approximate Solutions of Nonlinear Partial Differential Equations by Modifiedq-Homotopy Analysis Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Shaheed N. Huseen ◽  
Said R. Grace
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
Power Series Solution ◽  
Analysis Method ◽  
Exactly Solvable ◽  
Homotopy Analysis

A modifiedq-homotopy analysis method (mq-HAM) was proposed for solvingnth-order nonlinear differential equations. This method improves the convergence of the series solution in thenHAM which was proposed in (see Hassan and El-Tawil 2011, 2012). The proposed method provides an approximate solution by rewriting thenth-order nonlinear differential equation in the form ofnfirst-order differential equations. The solution of thesendifferential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

scholarly journals Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Flow ◽  
Finite Radius ◽  
Similarity Transformations ◽  
Moving Cylinder ◽  
Micropolar Nanofluid ◽  
Homotopy Analysis ◽  
Flow Phenomena

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.

Stagnation Flow of a Jeffrey Fluid over a Shrinking Sheet

2010 ◽  
Vol 65 (6-7) ◽  
pp. 540-548 ◽  
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Majid K
Keyword(s):  
Jeffrey Fluid ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Governing Equations ◽  
Stagnation Flow ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Equations Of Motions

January 22, 2009 The present paper describes the analytical solutions for the steady boundary layer flow of a Jeffrey fluid over a shrinking sheet. The governing equations of motions are reduced into a set of nonlinear ordinary differential equations by using similarity transformations. Two types of problems, namely, (1) two-dimensional stagnation flow towards a shrinking sheet and (2) axisymmetric stagnation flow towards an axisymmetric shrinking sheet, have been discussed. The series solutions of the problems are obtained by using the homotopy analysis method (HAM). The convergence of the obtained series solutions are analyzed and discussed in detail through graphs for various parameters of interest.

scholarly journals Unsteady two-layered fluid flow of conducting fluids in a channel between parallel porous plates under transverse magnetic field in a rotating system

2016 ◽  
Vol 21 (2) ◽  
pp. 423-446 ◽  
Author(s):  
T. Linga Raju ◽  
B. Neela Rao
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Differential Equations ◽  
Taylor Number ◽  
Rotating System ◽  
Electrically Conducting ◽  
Electrical Conductivities ◽  
Secondary Velocity ◽  
Conducting Fluids ◽  
Layered Fluid

AbstractAn unsteady MHD two-layered fluid flow of electrically conducting fluids in a horizontal channel bounded by two parallel porous plates under the influence of a transversely applied uniform strong magnetic field in a rotating system is analyzed. The flow is driven by a common constant pressure gradient in a channel bounded by two parallel porous plates, one being stationary and the other oscillatory. The two fluids are assumed to be incompressible, electrically conducting with different viscosities and electrical conductivities. The governing partial differential equations are reduced to the linear ordinary differential equations using two-term series. The resulting equations are solved analytically to obtain exact solutions for the velocity distributions (primary and secondary) in the two regions respectively, by assuming their solutions as a combination of both the steady state and time dependent components of the solutions. Numerical values of the velocity distributions are computed for different sets of values of the governing parameters involved in the study and their corresponding profiles are also plotted. The details of the flow characteristics and their dependence on the governing parameters involved, such as the Hartmann number, Taylor number, porous parameter, ratio of the viscosities, electrical conductivities and heights are discussed. Also an observation is made how the velocity distributions vary with the rotating hydromagnetic interaction in the case of steady and unsteady flow motions. The primary velocity distributions in the two regions are seen to decrease with an increase in the Taylor number, but an increase in the Taylor number causes a rise in secondary velocity distributions. It is found that an increase in the porous parameter decreases both the primary and secondary velocity distributions in the two regions.

scholarly journals Analytical solution of MHD free convective flow of couple stress fluid in an annulus with Hall and ion-slip effects

2011 ◽  
Vol 16 (4) ◽  
pp. 477-487 ◽  
Author(s):  
Darbhashayanam Srinivasacharya ◽  
Kolla Kaladhar
Keyword(s):  
Differential Equations ◽  
Couple Stress ◽  
Circular Cylinders ◽  
Couple Stress Fluid ◽  
Electrically Conducting ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Ion Slip

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and  temperature are discussed and shown graphically.

scholarly journals The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

2021 ◽  
Author(s):  
Vijay Patel ◽  
Jigisha Pandya
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

scholarly journals Serious Solutions for Unsteady Axisymmetric Flow over a Rotating Stretchable Disk with Deceleration

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 96 ◽  
Author(s):  
Sadiq
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Axisymmetric Flow ◽  
Analysis Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Rotating Stretchable Disk ◽  
Comparison Table

In this article, the author has examined the unsteady flow over a rotating stretchable disk with deceleration. The highly nonlinear partial differential equations of viscous fluid are simplified by existing similarity transformation. Reduced nonlinear ordinary differential equations are solved by homotopy analysis method (HAM). The convergence of HAM solutions is also obtained. A comparison table between analytical solutions and numerical solutions is also presented. Finally, the results for useful parameters, i.e., disk stretching parameters and unsteadiness parameters, are found.

Rotating Flow of a Micropolar Fluid Induced by a Stretching Surface

2010 ◽  
Vol 65 (10) ◽  
pp. 829-843 ◽  
Author(s):  
Tariq Javed ◽  
Iftikhar Ahmad ◽  
Zaheer Abbas ◽  
Tasawar Hayat
Keyword(s):  
Differential Equations ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Series Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Homotopy Analysis ◽  
Layer Flow

This investigation deals with the boundary layer flow of a micropolar fluid over a stretching surface. The flow is considered in a rotating frame of reference. The governing nonlinear partial differential equations are reduced to coupled nonlinear ordinary differential equations. The set of similarity equations has been solved analytically employing the homotopy analysis method (HAM). The series solutions are given for velocity and microrotation, and the convergence of these solutions are explicitly discussed. Attention has been focused to the variations of the emerging parameters on the velocity and microrotation are discussed through graphs.

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