On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model

Khan, Masood; Ali, S. Hyder; Qi, Haitao

doi:10.1016/j.nonrwa.2008.04.015

Cited by 75 publications

(37 citation statements)

References 32 publications

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“…Arshad 31 used unsteady MHD flow due to stretching surfaces and porous boundaries with no-slip condition. Salah et al 32 Khan et al 33 analysed the accelerated fluid flow, which is very close to the proposed model of this manuscript. Takhar et al 34 analyzed MHD flow for rotating fluid without slippage.…”

Section: Introductionsupporting

confidence: 77%

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

et al. 2014

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Magneto-Hydrodynamic (MHD) flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

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Section: Introductionsupporting

confidence: 77%

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

et al. 2014

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“…In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method will be used. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] …”

Section: Development Of the Governing Equationsmentioning

confidence: 99%

“…In general, fractional model of viscoelastic fluids is derived from well known ordinary model by replacing the ordinary time derivatives to fractional order time derivatives and this plays an important role to study the valuable tool of viscoelastic properties. Some authors [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] have investigated unsteady flows of fractionalized viscoelastic second grade, Maxwell, Oldroyed-B, Burgers' and generalized Burgers' model through walls/channel/ annulus and solutions for velocity field and the associated shear stress are obtained by using discrete Laplace transform, Fourier transform, Weber transform and finite Hankel transforms.…”

Section: Introductionmentioning

confidence: 99%

Helical flows of fractionalized Burgers' fluids

Jamil

Khan

2012

AIP Advances

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The unsteady flows of Burgers’ fluid with fractional derivatives model, through a circular cylinder, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Ut. The solutions that have been obtained, presented in series form in terms of the generalized Ga,b,c(•, t) functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for fractionalized Oldroyd-B, Maxwell and second grade fluids appear as special cases of the present results. Furthermore, the solutions for ordinary Burgers’, Oldroyd-B, Maxwell, second grade and Newtonian performing the same motion, are also obtained as special cases of general solutions by substituting fractional parameters α = β = 1. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison among models, is shown by graphical illustrations

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“…The primary advantage of such models is the introduction of a parameter, α, which can be used to model non-Markovian behavior of spatial or temporal processes. During the last decade, this approach has emerged as generalizations of many classic problems in mathematical physics, including the fractional Burgers' equation [11,25], the fractional Navier-Stokes equation [7,6], the fractional Maxwell equation [10], the fractional Schrödinger equation [8], the fractional Ginzburg Landau equation [8,22], etc. In parallel, numerical methods for classical differential equations, such as finite difference methods [15,14,23], finite element methods [3], spectral methods [13,2,12], and discontinuous Galerkin methods [19,24], have been developed, albeit this remains a relatively new topic of research.…”

Section: Introductionmentioning

confidence: 99%

A multi-domain spectral method for time-fractional differential equations

Chen

Hesthaven

2015

Journal of Computational Physics

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This paper proposes an approach for high-order time integration within a multi-domain setting for timefractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

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On accelerated flows of a viscoelastic fluid with the fractional Burgers’ model

Cited by 75 publications

References 32 publications

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Helical flows of fractionalized Burgers' fluids

A multi-domain spectral method for time-fractional differential equations

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