Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems

Chowdhury, Md. Sazzad Hossien; Hashim, Ishak; Abdul-Aziz, O. I.

doi:10.1016/j.cnsns.2007.09.005

Cited by 81 publications

(43 citation statements)

References 28 publications

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“…This method has been successfully applied to many non-linear problems, cf. [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Numerical results are presented graphically and are found to be in excellent agreement with the solutions of Cheng [3].…”

Section: Introductionsupporting

confidence: 75%

Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method

Bataineh

Noorani

Hashim

2008

Numerical Methods in Fluids

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SUMMARYIn this paper, we reconsider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The resulting boundary-value problem is solved analytically by the homotopy analysis method. The accuracy of the present solution is found to be in excellent agreement with the solutions of Cheng (Int. Commun. Heat Mass Transfer 2006; 33:627-635).

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Section: Introductionsupporting

confidence: 75%

Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method

Bataineh

Noorani

Hashim

2008

Numerical Methods in Fluids

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“…This method is a reliable analytical tool and it has already been applied to several interesting problems [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. It contains the frequently used analytical tools, namely, homotopy perturbation method (HPM) [23], -expansion method and adomian decomposition method [31].…”

Section: Introductionmentioning

confidence: 99%

Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet

Hayat

Mustafa

Shehzad

et al. 2011

Numerical Methods in Fluids

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SUMMARYThe steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upperconvected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number ( ) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter.

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“…The comparison between HAM and HPM can be found in [51,53]. According to (9), the governing equation can be deduced from the zero-order deformation (7).…”

Section: Analysis Of the Homotopy Analysis Methodsmentioning

confidence: 99%

“…This method has been successfully applied to solve many types of nonlinear problems by several authors [14, 15, 23 -25, 44, 49 -59]. Abbasbandy [51] has investigated an approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by using HAM. Nonlinear fin-type problems have been studied by Chowdhury et al [51].…”

Section: Introductionmentioning

confidence: 99%

“…Abbasbandy [51] has investigated an approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by using HAM. Nonlinear fin-type problems have been studied by Chowdhury et al [51]. This method is used to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity [52].…”

Section: Introductionmentioning

confidence: 99%

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Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

Dehghan

Manafian

Saadatmandi

2010

Zeitschrift Für Naturforschung A

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In this paper, the homotopy analysis method is applied to solve linear fractional problems. Based on this method, a scheme is developed to obtain approximation solution of fractional wave, Burgers, Korteweg-de Vries (KdV), KdV-Burgers, and Klein-Gordon equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for partial differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

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Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems

Cited by 81 publications

References 28 publications

Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method

Solution of fully developed free convection of a micropolar fluid in a vertical channel by homotopy analysis method

Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet

Key words: Nonlinear Differential-Difference Equations; Exp-Function Method; N-Soliton Solutions

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