Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet

Ghotbi, Abdoul R.

doi:10.1016/j.cnsns.2008.08.006

Cited by 27 publications

(17 citation statements)

References 22 publications

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“…Assuming a constant pressure, and neglecting the magnetic pressure term, the governing continuity and momentum equations (see Ghotbi [46]) are where u and v are the velocity components in the x and y directions, respectively, with the x-axis chosen along the stretching sheet, is the kinematic viscosity, is the fluid density, and is the electrical conductivity of the fluid. Following [29,30,43], the strength of the spatially varying magnetic field B(x) is taken as…”

Section: Problem Formulationmentioning

confidence: 99%

On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique

Motsa

Sibanda

2011

Numerical Methods in Fluids

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SUMMARY The problem of magneto‐hydrodynamic fluid flow past a nonlinear stretching sheet in the presence of a transverse magnetic field is analyzed. The governing equations are transformed into a nonlinear ordinary differential equation that is solved using a novel spectral homotopy analysis method and the Matlab in‐built numerical solverttbvp4c. The new technique removes some known limitations of the homotopy analysis method and offers a more systematic way of selecting initial approximations and the optimal auxiliary parameter ℏ. A comparison with the numerical solution confirms the robustness, the computational efficiency, and the accuracy of the technique. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Problem Formulationmentioning

confidence: 99%

On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique

Motsa

Sibanda

2011

Numerical Methods in Fluids

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“…The results of the velocity distributions for different values of the magnetic parameter M and the non linear parameter β are presented in graphs, while the values of the skin friction coefficients for some values of the parameters are given in a table. Table 1 and Table 2 show the values of the skin friction coefficient those of Hayat [24] and Abdoul [25]. The comparison revealed good agreement.…”

Section: Resultsmentioning

confidence: 64%

“…The paper is outlined as follows, in Section 2 the problem is formulated and the similarity transformation is used to reduce the formulated partial differential equation in to a non linear ordinary differential equation and a Keller box method is used to solve the problem; in Section 3 the resulted solutions are discussed in detail both numerically and graphically and the solutions are compared with the analytic solution of the same problems done by Hayat [24] using the modified decomposition method and Pade approximation; and by Abdoul [25] using homotopy analysis method (HAM). Finally in Section 4, some concluding remarks are given.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic Flow of Viscous Fluid over a Non-Linearly Stretching Sheet

Yirga¹,

Tesfay²

2014

OALib

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In this paper, the Magnetohydrodynamic (MHD) Flow of Viscous Fluid over a Nonlinear StretchingSheet is investigated numerically. The partial differential equations governing the flow are reduced to a non linear ordinary differential equations by using similarity transformations. The resulting transformed equations are numerically solved by an explicit finite difference scheme known as the Keller Box Method. The velocity profiles are determined and the effects of the magnetic parameter and non linear stretching parameter on the flow characteristics are investigated. In addition to this the numerical results for the local skin friction coefficients are computed. Comparison with the exact solution and previously reported analytic solutions is made and excellent agreement is noted. Moreover, the velocity profile obtained by Keller box method is in a better agreement to the exact solution than by the Homotopy Analysis Method. It is also found that, an increase in the magnetic parameter or non-linearity parameter causes a decrease in the velocity profile and velocity distribution.

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“…Mehmood et al [11] reported the corrections to HAM results presented in [10]. A comparison between their HAM solution and the exact solution obtained by Pavlov [12] was made and it was in a good agreement.…”

Section: Introductionmentioning

confidence: 81%

“…Ghotbi [10] considered the problem of the boundary layer flow of an incompressible viscous fluid over a nonlinear stretching sheet. In order to obtain analytical solution of the governing nonlinear differential equations, HAM is applied.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet

Hassan¹

2015

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This work deals with the boundary layer flow and heat transfer of an electrically conducting viscous fluid over a stretching sheet. Lie-group method is applied for determining the symmetry reductions for the governing equations by reducing the number of independent variables in the given system of partial differential equations by one, leading to a system of non-linear ordinary differential equation. The resulting system is then solved numerically using shooting method coupled with Runge-Kutta scheme. Effects of various values of physical parameters on the horizontal and vertical velocities, temperature profiles, wall heat transfer and the wall shear stress (skin friction), have been studied and the results are plotted. Furthermore, a comparison between the present results with existing numerical and homotopy methods has been reported and we found that they are in a good agreement.

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Homotopy analysis method for solving the MHD flow over a non-linear stretching sheet

Cited by 27 publications

References 22 publications

On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique

On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi‐analytical technique

Magnetohydrodynamic Flow of Viscous Fluid over a Non-Linearly Stretching Sheet

Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet

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