Explicit solution for some generalized fluids in laminar flow with slip boundary conditions

Chamekh, Mourad; Elzaki, Tarig M.

doi:10.22436/jmcs.018.03.03

Cited by 17 publications

(12 citation statements)

References 16 publications

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“…For details, one may see the monographs of Kilbas et al [1], some fundamental works on various aspects of fractional calculus are given by Kiryakova [2], Lakshmikantham and Vatsala [3], Miller and Ross [4] and the solutions method of differential equations of arbitrary real order and applications of the described methods in various fields are given by Podlubny [5]. In recent years, many analytical and approximate methods for solving fractional differential equations have been developed such as differential transform method [6,7], finite difference method (FDM) [8], Adomian decomposition method (ADM) [9,10], homotopy perturbation method (HPM) [11][12][13], Haar wavelet method (HWM) [14,15], differential transform method (DTM) [16][17][18], variational iteration method (VIM) [19] and many others. Among all the above-listed methods, homotopy perturbation method which was first proposed by the Chinese researcher J.H.…”

Section: Introductionmentioning

confidence: 99%

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

Jena

2018

SN Appl. Sci.

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In this article, a hybrid technique called homotopy perturbation Elzaki transform method has been applied to solve Navier-Stokes equation of fractional order. In the hybrid technique, homotopy perturbation method and Elzaki transform method are amalgamated. Three example problems are solved with a purpose to validate and demonstrate the efficacy of the present method. It is also demonstrated that the results obtained from the present method are in excellent agreement with the results by other methods. It is shown that the proposed method is found to be reliable, efficient and easy to implement for various related problems of science and engineering.non-linear partial differential equations are also solved by different authors [22,23] using modified HPM. The primary equation of movement of viscous fluid flow known as the NS equation has been presented in 1822 [24]. This equation portrays a few projections which include sea streams, fluid stream in channels, bloodstream and wind current around the wings of an airship. The NS equation was first carried out in 2005 in the fractional form in [25] by El-Shahed and Salem. The classical NS equation was answered by El-Shahed and Salem [25] by means of laplace transform (LT), finite Hankel transforms (FHT) and Fourier sine transform. A nonlinear fractional NS equation was solved analytically by Kumar et al. [26] by the combination of HPM with LT algorithm. Also the same NS equation was resolved by Ragab et al. [27] and Ganji et al. [28] by adopting homotopy analysis method. ADM was adopted by Birajdar [29] and Momani et al. [30] for the solution of fractional NS equation. Sunil Kumar et al. [31] achieved the analytical result of fractional NS equation by means of ADM and LT algorithm while Chaurasia and Kumar [32] solved the similar equation by the pairing of LT with FHT. The present paper gives an exact or approximate solution for the proposed problem by using HPETM.This article is planned as follows: some basic features of fractional calculus related to the titled problems have been presented in Sect. 2. Elzaki transform and elaborated form of the HPETM have been included in Sects. 3 and 4 respectively. In Sect. 5, three example problems are included to validate the effectiveness and exactness of the proposed method. Lastly, a conclusion is given in Sect. 6. Basic features of fractional calculusDefinition 2.1 The operator D of order in Abel-Riemann (A-R) sense is defined as [4,5,40] where m ∈ Z + , ∈ R + and Definition 2.2 The A-R fractional order integration operator J is described as [4,5]

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Section: Introductionmentioning

confidence: 99%

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

Jena

2018

SN Appl. Sci.

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“…Recently, mathematicians have had much attention for the approximate and analytical solutions of FDEs and had developed important mathematical techniques to solve FDEs. The well-known techniques regarding the solution of FDEs are the Adomian decomposition method (ADM) [25,26], finite difference method (FDM) [27], the differential transform method (DTM) [28,29], the homotopy perturbation transform method (HPTM) [30][31][32], the Haar wavelet method (HWM) [33,34], the differential transform method (DTM) [35][36][37], the variational iteration transform method (VIM) [38] and many others.…”

Section: Introductionmentioning

confidence: 99%

An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

Hajira

Khan

et al. 2020

Adv Differ Equ

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In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.

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“…Batista [6] succeeded in finding a closed form for the velocity components regarding the fluid flow between two uniformly co-rotating disks. Also, explicit solutions have been presented for generalized non-Newtonian fluids at different conditions with both mechanical and biological applications [7][8][9]. The flow of non-Newtonian power-law fluids considering the influence of a magnetic field has been studied [10][11][12] using the extensions of Karman analysis which discussed in [13,14].…”

Section: Introductionmentioning

confidence: 99%

Non-linear heat and mass transfer in a thermal radiated MHD flow of a power-law nanofluid over a rotating disk

et al. 2019

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The steady MHD flow of a power law nanofluid due to a uniform rotation of an infinite disk is studied with heat and mass transfer. The viscous dissipation has been comprised in the energy equation. The governing PDEs are reduced to a set of ODEs; using the generalized Von Karman similarity transformations; for which finite difference numerical scheme is implemented along with the associated boundary conditions. The non-Newtonian fluid characteristics affect the fluid velocity, temperature and concentration of suspended nanoparticles. The significant effects of thermal radiation, Brownian motion and thermophoresis diffusion are involved. The skin friction coefficients in addition to the heat and mass transfer rates are defined and calculated considering the variation of all flow parameters. The present results are verified and compared with literature.

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Explicit solution for some generalized fluids in laminar flow with slip boundary conditions

Cited by 17 publications

References 16 publications

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

Solving time-fractional Navier–Stokes equations using homotopy perturbation Elzaki transform

An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

Non-linear heat and mass transfer in a thermal radiated MHD flow of a power-law nanofluid over a rotating disk

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