Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects

Roohi, Reza; Heydari, Mohammad Hossein; Bavi, Omid; Emdad, Homayoun

doi:10.1007/s00366-019-00843-9

Cited by 46 publications

(19 citation statements)

References 33 publications

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“…[18][19][20][21][22] The nonsingularity of kernels of such operators allows us to provide appropriate numerical methods with high accuracy and stability for solving problems involving these types of operators and enables us to examine different phenomena in Engineering and Physics with great accuracy. 23,24 We remind that during the last decades, many studies have been done on the topic of variable-order (VO) fractional calculus (differentiation and integration of VO), its applications in Physics and Engineering, [25][26][27] and the numerical solution of problems involving such operators, especially nonsingular ones. In Hosseininia et al, 28 a meshfree technique is applied for VO fractional reaction-diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

“…We remind that during the last decades, many studies have been done on the topic of variable‐order (VO) fractional calculus (differentiation and integration of VO), its applications in Physics and Engineering, 25‐27 and the numerical solution of problems involving such operators, especially nonsingular ones. In Hosseininia et al, 28 a meshfree technique is applied for VO fractional reaction‐diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation

Heydari

Avazzadeh

Cattani

2020

Math Methods in App Sciences

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In this article, nonlinear variable-order (VO) fractional Korteweg-de Vries (KdV) Burgers' equation with nonsingular VO time fractional derivative is introduced and discussed. The approximate solution of the expressed problem is obtained in the form of a series expansion in terms of the shifted discrete Chebyshev polynomials (CPs) with great accuracy. The method is a computational procedure based on the collocation technique and the shifted discrete CPs together with their operational matrices (ordinary and VO fractional derivatives). The main advantage of the designed approach is that it provides a global solution for the problem. In order to examine the efficiency of the designed algorithm, some numerical problems have been provided. The obtained solutions confirm that the present method is computationally effective and sufficiently accurate in solving this equation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation

Heydari

Avazzadeh

Cattani

2020

Math Methods in App Sciences

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“…The fractional calculus of variable order (VO) as an useful mathematical framework deals with derivative and integral operators of VO fractional orders 1 . It is shown that systems modeled by this new concept are more precise and sensitive than the ones modeled by the constant‐order fractional calculus 2‐5 . Recently, the issue of singularity in fractional derivative and integral operators has attracted the interest of some researchers to define nonsingular fractional operators, for example, see other studies 6‐8 .…”

Section: Introductionmentioning

confidence: 99%

“…1 It is shown that systems modeled by this new concept are more precise and sensitive than the ones modeled by the constant-order fractional calculus. [2][3][4][5] Recently, the issue of singularity in fractional derivative and integral operators has attracted the interest of some researchers to define nonsingular fractional operators, for example, see other studies. [6][7][8] Presumably, differential equations with nonsingular fractional derivatives can model phenomena more precisely than the singular ones.…”

Section: Introductionmentioning

confidence: 99%

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

Heydari

Avazzadeh

2020

Math Methods in App Sciences

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This article defines a novel version of nonlinear fourth‐order diffusion‐wave equation, which involves variable‐fractional differentiations with nonsingular kernel. This newly defined equation entails a highly accurate method for its numerical solution. The proposed scheme is based upon the orthonormal Bernstein polynomials and their operational matrices of variable‐order fractional differentiation together with the collocation method. In this paper, the formulation for obtaining these operational matrices are provided in details. The method converts the original problem to a system of algebraic equations that can be promptly solved using a software program. To clarify the validity and the high precision of the devised method, numerous illustrative examples with various boundary conditions are examined.

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“…The non-Newtonian viscoelastic fluid between parallel oscillating plates occurs in several applications namely, lubrication of mechanical devices, biomedical engineering and oil industry [10]. Fluid near the plates would oscillate harmonically with the plate in similar time period, while the amplitude of fluid motion rises slowly across the direction of the guiding surface.…”

Section: Introductionmentioning

confidence: 99%

A numerical study on nonlinear dynamics of oscillatory time-depended viscoelastic flow between infinite parallel plates: utilization of symmetric and antisymmetric Chandrasekhar functions

Roohi

Ashrafi

Samghani

et al. 2019

Heliyon

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The one-dimensional viscoelastic fluid flow between two infinite parallel plates with oscillatory inlet condition is examined using the Johnson–Segalman model. The symmetric and antisymmetric Chandrasekhar functions in space are utilized to represent the velocity and stress fields. The non-dimensional form of the conservation laws in addition to the constitutive equations are solved numerically based on the Galerkin projection method. Two critical Weissenberg numbers (We) for various Reynolds numbers (Re) and viscosity ratios (ε) are obtained to determine the stable range of nonlinear system behavior. Moreover, for the unsteady case, the effects of Re, viscosity ratio of solvent to solution as well as We are investigated. According to the obtained results, increasing of oscillations frequency in subcritical zone, the same as low frequency case, has almost no effect on the velocity and its gradient. Nevertheless, the normal stress amplitude of oscillations is reduced. The Re number determines the number of oscillations and the needed time prior to the steady condition. For lower Re, due to higher effect of viscosity, the initial fluctuations are intensely occurred in a short time period in contrary to the high Re case.

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Chebyshev polynomials for generalized Couette flow of fractional Jeffrey nanofluid subjected to several thermochemical effects

Cited by 46 publications

References 33 publications

Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation

Discrete Chebyshev polynomials for nonsingular variable‐order fractional KdV Burgers' equation

Orthonormal Bernstein polynomials for solving nonlinear variable‐order time fractional fourth‐order diffusion‐wave equation with nonsingular fractional derivative

A numerical study on nonlinear dynamics of oscillatory time-depended viscoelastic flow between infinite parallel plates: utilization of symmetric and antisymmetric Chandrasekhar functions

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