MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method

Pahlavan, Amir A.; Aliakbar, Vahid; Vakili-Farahani, Farzad; Sadeghy, Kayvan

doi:10.1016/j.cnsns.2007.09.011

Cited by 61 publications

(37 citation statements)

References 35 publications

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“…We have considered the effects of flow parameters such as Grashof number Gr (buoyancy effects), Hartmann number M(magnetic field parameter), thermal radiation parameter N R , suction/injection parameter R, and heat source ðD > 0Þ or a heat sink ðD < 0Þ in the boundary layer and the flow behaviour on the velocity and temperature fields. We have extended the scope and applicability of earlier results by Chamkha [35], Abel [32], Makinde and Ogulu [34], Shateyi [28] and Seddeek [37] to porous sheet and using homotopy analysis method (HAM) to solve the problem using two axillary parameters by Alizadeh-Pahlavan et al [43]. In our results, it was found that when the buoyancy parameter increases, the fluid velocity increases and the thermal boundary layer decreases.…”

Section: Resultssupporting

confidence: 54%

Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method

Daniel

2015

Alexandria Engineering Journal

130

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This paper investigates the theoretical influence of buoyancy and thermal radiation on MHD flow over a stretching porous sheet. The model which constituted highly nonlinear governing equations is transformed using similarity solution and then solved using homotopy analysis method (HAM). The analysis is carried out up to the 5th order of approximation and the influences of different physical parameters such as Prandtl number, Grashof number, suction/injection parameter, thermal radiation parameter and heat generation/absorption coefficient and also Hartman number on dimensionless velocity, temperature and the rate of heat transfer are investigated and discussed quantitatively with the aid of graphs. Numerical results obtained are compared with the previous results published in the literature and are found to be in good agreement. It was found that when the buoyancy parameter and the fluid velocity increase, the thermal boundary layer decreases. In case of the thermal radiation, increasing the thermal radiation parameter produces significant increases in the thermal conditions of the fluid temperature which cause more fluid in the boundary layer due to buoyancy effect, causing the velocity in the fluid to increase. The hydrodynamic boundary layer and thermal boundary layer thickness increase as a result of increase in radiation. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Section: Resultssupporting

confidence: 54%

Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method

Daniel

2015

Alexandria Engineering Journal

130

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“…Different from approximations given by perturbation methods or other nonperturbation techniques, our series solutions (28), (29) and (30) contain the auxiliary parameter , which provides us with a simple way to control and adjust the convergence of the series solution, as shown by Liao [17,18,19,20,21,22] and others [23,24,25,26,27,28,29,30,31,32,33]. However, physically speaking, the wave phase speed c and the wave surface η(x) are dependent upon the physical parameters H and only, having nothing to do with the auxiliary parameter .…”

Section: Results Analysismentioning

confidence: 99%

“…Among them, the so-called homotopy analysis method (HAM) [17,18,19,20,21,22] is rather attractive, which has been successfully applied to many aspects of nonlinear problems [23,24,25,26,27,28,29,30,31,32,33]. In the field of the wave propagation, Liao and Cheung [19] used the homotopy analysis method to give high-order convergent series solutions for the dispersion relationship of the deep water waves.…”

Section: Introductionmentioning

confidence: 99%

On the interaction of deep water waves and exponential shear currents

Cheng

Cang

Liao

2008

Z. angew. Math. Phys.

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A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil-Jacotin transformation is used to transfer the original exponentially nonlinear boundaryvalue problem in an unknown domain into an algebraically nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest, but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves on a shear current: a train of propagating waves on a shear current breaks as the fluid velocity at crest equals the wave phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering.

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“…Also, it is easy to be proceed to high order. Because of these features, the HAM has been widely applied to many aspects of nonlinear science, see for instance [16][17][18][19][20][21][22][23][24]. …”

Section: Appendix a Brief Description Of The Hammentioning

confidence: 99%

A short comment on the effect of a shear layer on nonlinear water waves

Cang

Cheng

Grimshaw

2010

Sci. China Phys. Mech. Astron.

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In this paper we study nonlinear periodic deep water waves propagating on a background shear current, which decays exponentially with depth. We extend the study of Cheng, Cang and Liao (2009) by introducing a second parameter which measures the depth of the shear current. A high-order convergent analytical series solution is obtained by the homotopy analysis method (HAM). A detailed analysis of the impact of the depth parameter is given. We find that increasing this parameter so that the shear current is thinner reduces the wave phase speed, smoothes the wave crest, sharpens the trough, and enlarges the maximum wave height for the case of propagating waves on an opposing current; while it produces the opposite effect on an aiding current.nonlinear water waves, wave-current interaction, homotopy analysis method

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MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method

Cited by 61 publications

References 35 publications

Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method

Effects of buoyancy and thermal radiation on MHD flow over a stretching porous sheet using homotopy analysis method

On the interaction of deep water waves and exponential shear currents

A short comment on the effect of a shear layer on nonlinear water waves

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