Analytic Approximations for the Flow Near the Equator of a Steady Magnetohydrodynamic Boundary Layer Over a Rotating Sphere

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
A. El-Nahhas
Keyword(s):  
Boundary Layer ◽  
Analysis Method ◽  
Radial Magnetic Field ◽  
Rotating Sphere ◽  
Electrically Conducting ◽  
Strongly Nonlinear ◽  
Analytic Approximations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Steady Laminar

The strongly nonlinear problem for the steady, laminar, viscous incompressible ,and electrically conducting fluid near the equator of the boundary layer flow due to a rotating sphere and in the presence of a uniform radial magnetic field is considered. Analytic approximations for this problem are obtained through the application of the homotopy analysis method and via a fractional basis. Variations for velocity and temperature profiles with the change of the suction/blowing, rotational, and magnetic parameters are studied.

scholarly journals Homotopy Analysis Decomposition Method for the Solution of Viscous Boundary Layer Flow Due to a Moving Sheet

2019 ◽  
pp. 1-7
Author(s):  
S. Alao ◽  
R. A. Oderinu ◽  
F. O. Akinpelu ◽  
E. I. Akinola
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Analysis Method ◽  
Viscous Boundary Layer ◽  
New Approach ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Viscous Boundary ◽  
Adomian Polynomial

This paper investigates a new approach called Homotopy Analysis Decomposition Method (HADM) for solving nonlinear differential equations, the method was developed by incorporating Adomian polynomial into Homotopy Analysis Method. The Adomian polynomial was used to decompose the nonlinear term in the equation then apply the scheme of homotopy analysis method. The accuracy and efficiency of the proposed method was validated by considering algebraically decaying viscous boundary layer  flow due to a moving sheet. Diagonal Pade approximation was used to get the skin friction. The obtained results were presented along with other methods in the literature in tabular form to show the computational efficiency of the new approach. The results were found to agree with those in literature. Owing to its small size of computation, the method is not aected by discretization error as the results are presented in form of polynomials.

Nonlinear Stretching Flow with Thermal Radiation

2010 ◽  
Vol 65 (10) ◽  
pp. 761-770
Author(s):  
Tasawar Hayat ◽  
Rabia Noureen ◽  
Tariq Javed
Keyword(s):  
Radiation Effects ◽  
Temperature Fields ◽  
Porous Space ◽  
Analysis Method ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Rotating Boundary ◽  
Nonlinear Stretching ◽  
Stretching Flow

This work concerns with the radiation effects on rotating boundary layer flow of an electrically conducting incompressible fluid over a nonlinear stretching surface. The viscous fluid fills the porous space. The flow is permeated by a constant magnetic field applied in the transverse direction. Two types of temperatures are prescribed to the surface. The resulting problems of velocity and temperature are obtained using the homotopy analysis method (HAM). Convergence of the developed series solutions is carefully checked. Graphical results of the velocity and temperature fields for various values of the parameters of the problems are presented and discussed.

Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

2014 ◽  
Vol 6 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Antonio Mastroberardino
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Layer Flow

AbstractAn investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

scholarly journals Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. Rashidi ◽  
E. Momoniat ◽  
B. Rostami
Keyword(s):  
Boundary Layer ◽  
Viscoelastic Fluid ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Electrically Conducting ◽  
Boundary Layer Equations ◽  
Homotopy Analysis ◽  
Energy Equations

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). It is clear that by the use of second auxiliary parameter, the straight line region inℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a) prescribed surface temperature (PST) and (b) prescribed heat flux (PHF). The effect of involved parameters on velocity and temperature is investigated.

scholarly journals Heat and Mass Transfer of Magnetohydrodynamics (MHD) Boundary Layer Flow using Homotopy Analysis Method

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 189-201 ◽  
Author(s):  
Nur Liyana Nazari ◽  
Ahmad Sukri Abd Aziz ◽  
Vincent Daniel David ◽  
Zaileha Md Ali
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Schmidt Number ◽  
Magnetic Parameter ◽  
Radiation Parameter ◽  
Analysis Method ◽  
Mhd Boundary Layer ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

Heat and mass transfer of MHD boundary-layer flow of a viscous incompressible fluid over an exponentially stretching sheet in the presence of radiation is investigated. The two-dimensional boundary-layer governing partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The transformed equations of momentum, energy and concentration are solved by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by comparing the HAM solution with existing solutions. The influence of physical parameters such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt number on velocity, temperature and concentration profiles are discussed. It is found that the increasing values of magnetic parameter reduces the dimensionless velocity field but enhances the dimensionless temperature and concentration field. The temperature distribution decreases with increasing values of Prandtl number. However, the temperature distribution increases when radiation parameter increases. The concentration boundary layer thickness decreases as a result of increase in Schmidt number

scholarly journals Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method

2010 ◽  
Vol 15 (1) ◽  
pp. 83-95 ◽  
Author(s):  
M. M. Rashidi ◽  
S. A. Mohimanian Pour
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Analysis Method ◽  
Unsteady Boundary Layer ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Layer Flow

In this work, the homotopy analysis method is applied to study the unsteady boundary-layer flow and heat transfer due to a stretching sheet. The analytic solutions of the system of nonlinear ordinary differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. The velocity and temperature profiles are shown and the influence of non-dimensional parameter on the heat transfer is discussed in detail. The validity of our solutions is verified by the numerical results.

scholarly journals Homotopy Analysis Method to determine Magneto Hydrodynamics flow of compressible fluid in a channel with porous walls

2016 ◽  
Vol 34 (1) ◽  
pp. 173-186
Author(s):  
Reza Mohammadyari ◽  
J. Rahimipetroudi ◽  
Iman Rahimipetroudi ◽  
Mazaher Rahimi Esboee
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Compressible Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Porous Walls ◽  
Layer Flow

In this article magnetohydrodynamics (MHD) boundary layer flow of compressible fluid in a channel with porous walls is researched. In this study it is shown that the nonlinear Navier-Stokes equations can be reduced to an ordinary differential equation, using the similarity transformations and boundary layer approximations. Analytical solution of the developed nonlinear equation is carried out by the Homotopy Analysis Method (HAM). In addition to applying HAM into the obtained equation, the result of the mentioned method is compared with a type of numerical analysis as Boundary Value Problem method (BVP) and a good agreement is seen. The effects of the Reynolds number and Hartman number are investigated.

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