Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge–Kutta Method

Ganji, Z. Z.; Ganji, D.D.

doi:10.1007/s11242-009-9421-2

Cited by 11 publications

(3 citation statements)

References 29 publications

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“…Berman (1953) analyzed the boundary layer flow of a Newtonian fluid through a porous channel through self similar exact solution. His solution was further generalized by several other researchers (Cox, 1991;Zaturska et al, 1988;Desseaus, 1999;Ganji and Ganji, 2010). Vajravelu and Kumar (2004) investigated axially symmetric hydromagnetic flow between two horizontal plates in a rotating system where the lower plate was a stretching sheet and the upper plate was subjected to uniform injection, with the help of numerical and analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

A series solution of the boundary value problem arising in the application of fluid mechanics

Khan

2018

HFF

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Purpose This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM). Design/methodology/approach The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs. Findings It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number. Originality/value To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

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Section: Introductionmentioning

confidence: 99%

A series solution of the boundary value problem arising in the application of fluid mechanics

Khan

2018

HFF

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“…One of the semi-exact methods which does not need small parameters is the differential transformation method (DTM). Therefore, same as the homotopy analysis (Moghimi et al, 2011;Bararnia et al, 2010;Ghotbi et al, 2009Ghotbi et al, , 2011Asgharian et al, 2010;Ghsemi et al, 2012), the homotopy perturbation method (Bararnia et al, 2011;Barari et al, 2008a, b;Sheikholeslami et al, 2011;Raftari and Yildirim, 2011;Miansari et al, 2010) and the Adomian decomposition method (Ganji et al, 2010(Ganji et al, , 2011Sheikholeslami et al, 2012), the DTM can overcome the restrictions and limitations of perturbation methods. This method constructs an analytical solution in the form of a polynomial.…”

Section: Introductionmentioning

confidence: 99%

Investigation of heat and mass transfer of rotating MHD viscous flow between a stretching sheet and a porous surface

Sheikholeslami

Ashorynejad

Barari

et al. 2013

Engineering Computations

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Purpose -The purpose of this paper is to analyze hydromagnetic flow between two horizontal plates in a rotating system. The bottom plate is a stretching sheet and the top one is a solid porous plate. Heat transfer in an electrically conducting fluid bounded by two parallel plates is also studied in the presence of viscous dissipation. Design/methodology/approach -Differential Transformation Method (DTM) is used to obtain a complete analytic solution for the velocity and temperature fields and the effects of different governing parameters on these fields are discussed through the graphs. Findings -The obtained results showed that by adding a magnetic field to this system, transverse velocity component reduces between the two plates. Also as the Prandtl number increases, in presence of viscous dissipation, the temperature between the two plates enhances while an opposite behavior is observed when the viscous dissipation is negligible. Originality/value -The equations of conservation of mass, momentum and energy are reduced to a non-linear ordinary differential equations system. Differential Transformation Method is utilized to approximate the solution for velocity and temperature profiles.

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“…Since there are some limitations with the common perturbation method, and also because the basis of the common perturbation method was based upon the existence of a small parameter, developing the method for different applications is very difficult. Therefore, many different new methods have recently been introduced allowing ways to eliminate the small parameter, such as the artificial parameter method (Liu, 1997), the homotopy analysis method (Liao, 1995), the variational iteration method (He, 1998a(He, , b, 1999bHe et al, 2010;Faraz et al, 2011), the Adomian decomposition method (Adomian, 1994;Wazwaz, 2006;Ganji and Ganji, 2010), the Laplace decomposition method (Khan, 2009), the homotopy perturbation transform method (Khan and Wu, 2011) and the differential transform method (Rashidi, 2009). One of the semi-exact methods is the homotopy perturbation method (HPM).…”

Section: Introductionmentioning

confidence: 99%

Application of homotopy perturbation and numerical methods to the circular porous slider

Madani¹,

Khan²,

Mahmodi³

et al. 2012

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to present the problem of three-dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate. Design/methodology/approach -The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained HPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results. Findings -Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered. Originality/value -Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Padé approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan-Thien techniques.

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Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge–Kutta Method

Cited by 11 publications

References 29 publications

A series solution of the boundary value problem arising in the application of fluid mechanics

A series solution of the boundary value problem arising in the application of fluid mechanics

Investigation of heat and mass transfer of rotating MHD viscous flow between a stretching sheet and a porous surface

Application of homotopy perturbation and numerical methods to the circular porous slider

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