Comment on “Solutions with special functions for time fractional free convection flow of Brinkman-type fluid” by F. Ali et al.

El-Lateif, A. M. Abd; Abdel-Hameid, A. M.

doi:10.1140/epjp/i2017-11706-3

Cited by 9 publications

(8 citation statements)

References 16 publications

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“…For the Cauchy stress tensor, Rivlin-Ericksen tensors, Darcy law and thermodynamic stability conditions of differential type second grade fluid (see [21] and references therein). e fractional formalism of thermal and concentration gradients can be seen in [45,46].…”

Section: Mathematical Descriptionmentioning

confidence: 99%

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

Anwar¹,

Irfan

Hussain

et al. 2022

Mathematical Problems in Engineering

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This study examines viscoelastic fractional nanofluid flow through Darcy medium. Memory characteristics due to elasticity are explored with noninteger time derivatives. The unsteady motion of MHD flow is modeled by nonlinear differential equations. Buoyancy forces are incorporated via convection parameters in the flow domain. Fractional relaxation time is considered to control the propagation speed of temperature. A finite difference, along with finite element, a numerical algorithm has been developed for the computation of governing flow equations. Friction coefficient, Sherwood numbers, and Nusselt numbers are computed for the noninteger derivative model. Simulations revealed that noninteger numbers have congruous behavior for concentration, temperature, and velocity fields. It is also noted that heat flux, δ 1 , and mass flux, δ 2 , numbers have contradictory effects on the friction coefficient. Various flows, particularly in polymer industries and electrospinning for the production of nanofibers, can be tackled in a comparable pattern.

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Section: Mathematical Descriptionmentioning

confidence: 99%

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

Anwar¹,

Irfan

Hussain

et al. 2022

Mathematical Problems in Engineering

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“…Hameid et al [27] applied the definition of the fractional order derivative to the convective part of a constitutive equation and explained their model in a very interesting way. Vieru et al [28] have followed the discussion presented by Hameid et al [27] by applying the fractional derivative definition in a constitutive equation. Keeping in mind all the above discussions, we present this article exploring the effect of side walls on the motion of an incompressible fluid using generalized fractional constitutive equations and the Caputo-Fabrizio derivative through a rectangular channel.…”

Section: Problem Formulationmentioning

confidence: 99%

“…This approach is appealing to mathematical and physical aspects of fluid mechanics. Hameid et al [27] applied the definition of the fractional order derivative to the convective part of a constitutive equation and explained their model in a very interesting way. Vieru et al [28] have followed the discussion presented by Hameid et al [27] by applying the fractional derivative definition in a constitutive equation.…”

Section: Introductionmentioning

confidence: 99%

Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative

et al. 2019

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In this article, unidirectional flows of fractional viscous fluids in a rectangular channel are studied. The flow is generated by the shear stress given on the bottom plate of the channel. The authors have developed a generalized model on the basis of constitutive equations described by the time-fractional Caputo–Fabrizio derivative. Many authors have published different results by applying the time-fractional derivative to the local part of acceleration in the momentum equation. This approach of the fractional models does not have sufficient physical background. By using fractional generalized constitutive equations, we have developed a proper model to investigate exact analytical solutions corresponding to the channel flow of a generalized viscous fluid. The exact solutions for velocity field and shear stress are obtained by using Laplace transform and Fourier integral transformation, for three different cases namely (i) constant shear, (ii) ramped type shear and (iii) oscillating shear. The results are plotted and discussed.

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“…In the present case, continuity equation is identically satisfied for the proposed velocity field and in-compressible flow is modeled by the following fractional differential equations [23,26,36,38] where is momentum memory effect, stands for density of the fluid, 1 , 1 and 2 denote the relaxation times, 2 stands for retardation time, T represents temperature, C denotes the concentration, is thermal memory effect, stands for diffusion memory effect, c p denotes specific heat, 1 is thermal…”

Section: Governing Partial Differential Equationsmentioning

confidence: 99%

“…Generalized Fick's law and Cattaneo-Maxwell model with non-integer time derivatives are used to incorporate relaxation times in concentration and energy equations [23][24][25]. Modification in these laws will help to control the sudden increase in propagation speed of thermal and diffusing quantities [26]. Here, Oldroyd-B fluid model is considered to analyze Joule heating effects in viscoelastic materials [27].…”

Section: Introductionmentioning

confidence: 99%

Joule heating in magnetic resistive flow with fractional Cattaneo–Maxwell model

Anwar

Rasheed

2018

J Braz. Soc. Mech. Sci. Eng.

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Influence of electric and magnetic fields in a nonlinear viscoelastic flow is studied in this communication. Microscopic description of Joule heating can be seen with the proposed model. Fractional formulation of the problem with Cattaneo-Maxwell model leads to oscillation and relaxation processes that show memory and delay of thermal and diffusing flux. Abrupt change in temperature and concentration in MHD flow can be controlled with this formalism. Time-dependent flow is governed by highly nonlinear fractional differential equations. Finite-element-finite-difference algorithm is used to solve the fractional coupled fields and flow dynamics problem. Remarkable physical parameters are calculated to signify the importance of problem under observation. Modeled problem can be tackled in numerous ways to obtain accurate simulations in polymer and electromagnetic casting industries.

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Comment on “Solutions with special functions for time fractional free convection flow of Brinkman-type fluid” by F. Ali et al.

Cited by 9 publications

References 16 publications

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo–Fabrizio Derivative

Joule heating in magnetic resistive flow with fractional Cattaneo–Maxwell model

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