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

Madani, Mohammad; Khan, Yasir; Mahmodi, Gh.; Faraz, Naeem; Yıldırım, Ahmet; Nasernejad, B.

doi:10.1108/09615531211244844

Cited by 11 publications

(10 citation statements)

References 54 publications

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“…In 2007, Momani and Odibat (2007) adopted the method for fractional differential equations with great success, and now it is an effective method for fractional calculus (Ganji et al, 2008;Gupta et al, 2012;Jafari and Momani, 2007;Liu, 2012;Madani et al, 2012;Odibat and Momani, 2008). In 2010, the Laplace transform and He's polynomials were used in the homotopy perturbation method (Khan and Mohyud-Din, 2010).…”

Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

Fractional calculus for nanoscale flow and heat transfer

Liu

2014

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

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If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation. AbstractPurpose -Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach -This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss' divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given. Findings -Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations. Originality/value -Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.

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Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

Fractional calculus for nanoscale flow and heat transfer

Liu

2014

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

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“…Ghoreishi studied the circular slider [14]. Madani investigated the circular porous slider by using HPM, and also analyzed its lift and drag [19].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Hydro-Magnetic Flow Arising in a Long Porous Slider and a Circular Porous Slider with Velocity Slip

et al. 2019

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The current research explores the injection of a viscous fluid through a moving flat plate with a transverse uniform magneto-hydrodynamic (MHD) flow field to reduce sliding drag. Two cases of velocity slip between the slider and the ground are studied: a long slider and a circular slider. Solving the porous slider problem is applicable to fluid-cushioned porous sliders, which are useful in reducing the frictional resistance of moving bodies. By using a similarity transformation, three dimensional Navier–Stokes equations are converted into coupled nonlinear ordinary differential equations. The resulting nonlinear boundary value problem was solved analytically using the homotopy analysis method (HAM). The HAM provided a fast convergent series solution, showing that this method is efficient, accurate, and has many advantages over the other existing methods. Solutions were obtained for the different values of Reynolds numbers (R), velocity slip, and magnetic fields. It was found that surface slip and Reynolds number had substantial influence on the lift and drag of the long and the circular sliders. Moreover, the effects of the applied magnetic field on the velocity components, load-carrying capacity, and friction force are discussed in detail with the aid of graphs and tables.

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“…Several analytical and numerical methods (Vanani and Aminataei, 2012;Abdou and Yildirim, 2012;Mohyud-Din et al, 2012;Yildirim and Koc¸ak, 2012) have been proposed to solve fractional differential equations. Such as, Adomian decomposition method (Adomian, 1988;Wazwaz and El-Sayed, 2001), variational iteration method (He, 1999;Wazwaz, 2009), differential transform method (Erturk et al, 2008;Erturk et al, 2012) and homotopy perturbation method (HPM) (He, 2003(He, , 2005Madani et al, 2012;Gupta et al, 2012;Khan et al, 2012). Odibat (Odibat, 2007;Odibat and Momani, 2008) presented an improvement of the HPM, and solved many more problems.…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions

Liu

Liang

2015

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

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Purpose – The purpose of this paper is to apply a new modified homotopy perturbation method, which is effective to solve multi-order fractional equations with non-polynomial initial and boundary conditions. Design/methodology/approach – The proposed algorithm is tested on multi-order fractional advection-dispersion equations. The fractional derivatives described in this paper are in the Caputo sense. Findings – Approximate results explicitly reveal the complete reliability, efficiency and accuracy of the new modified technique. Originality/value – It is observed that the approach may be implemented to other multi-fractional models with non-polynomial initial and boundary conditions.

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

Cited by 11 publications

References 54 publications

Fractional calculus for nanoscale flow and heat transfer

Fractional calculus for nanoscale flow and heat transfer

Three-Dimensional Hydro-Magnetic Flow Arising in a Long Porous Slider and a Circular Porous Slider with Velocity Slip

Approximate solutions of multi-order fractional advection-dispersion equation with non-polynomial conditions

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