Flow, heat and mass transfer of three-dimensional fractional Maxwell fluid over a bidirectional stretching plate with fractional Fourier’s law and fractional Fick’s law

Bai, Yu; Huo, Lamei; Zhang, Yan; Jiang, Yuehua

doi:10.1016/j.camwa.2019.04.027

Cited by 24 publications

(7 citation statements)

References 39 publications

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“…( ) as in [22], where k, n 1 and n 2 are constants. This function is employed to describe a two-dimensional problem and reveal the fact that in the process of infiltration, impurities in the fluid precipitate or accumulate, resulting in an uneven inner wall of the filter tube and a non-uniform fluid penetration.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Li et al [21] analyzed the flow and heat transfer of a power-law liquid food over a non-uniform penetrable channel. Bai et al [22] addressed the flow, heat, and mass transfer problem of Maxwell fluid past a bidirectional stretching sheet. The nonuniform suction/injection velocity of fluid flowing through the porous permeable plate was written as a specific function = v x t kt x y , ,…”

Section: Introductionmentioning

confidence: 99%

“…where k, n , 1 n 2 and n 3 are constants. We have adopted a function similar to that in [22] to describe the non-uniform permeation in this study. Furthermore, Mondal et al [23] studied the rheological model of non-Newtonian fluid migration in the ultrafiltration process of a juice.…”

Section: Introductionmentioning

confidence: 99%

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On the process of filtration of fractional viscoelastic liquid food

Meng¹,

Li²,

Si³

et al. 2021

Commun. Theor. Phys.

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In the process of filtration, fluid impurities precipitate/accumulate; this results in an uneven inner wall of the filter, consequently leading to non-uniform suction/injection. The Riemannian–Liouville fractional derivative model is used to investigate viscoelastic incompressible liquid food flowing through a permeable plate and to generalize Fick’s law. Moreover, we consider steady-state mass balance during ultrafiltration on a plate surface, and a fractional-order concentration boundary condition is established, thereby rendering the problem real and complex. The governing equation is numerically solved using the finite difference algorithm. The effects of the fractional constitutive models, generalized Reynolds number, generalized Schmidt number, and permeability parameter on the velocity and concentration fields are compared. The results show that an increase in fractional-order α in the momentum equation leads to a decrease in the horizontal velocity. Anomalous diffusion described by the fractional derivative model weakens the mass transfer; therefore, the concentration decreases with increasing fractional derivative γ in the concentration equation.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the process of filtration of fractional viscoelastic liquid food

Meng¹,

Li²,

Si³

et al. 2021

Commun. Theor. Phys.

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“…Then, Li et al (2016) investigated the flow and heat transfer of fractional Maxwell fluid between two infinite parallel plates with fractional Fourier's law. Bai et al (2019a) discussed heat and mass transfer of threedimensional fractional Maxwell fluid with fractional Fourier's law and fractional Fick's law. In addition, some scholars used generalized Fourier's law to describe thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time dependent stretching plate with generalized Fourier’s law

Bai

Huo

Zhang

2020

HFF

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Purpose The purpose of this study is to investigate the unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time power-law-dependent stretching plate. Based on the characteristics of pressure in the boundary layer, the momentum equation with the fractional Maxwell model is firstly formulated to analyze unsteady stagnation-point flow. Furthermore, generalized Fourier’s law is considered in the energy equation and boundary condition of convective heat transfer. Design/methodology/approach The nonlinear fractional differential equations are solved by the newly developed finite difference scheme combined with L1-algorithm, whose convergence is verified by constructing a numerical example. Findings Some interesting results can be revealed. The larger fractional derivative parameter of velocity promotes the flow, while the smaller fractional derivative parameter of temperature accelerates the heat transfer. The temperature boundary layer is thicker than the velocity boundary layer, and the velocity enlarges as the stagnation parameter raises. This is because when Prandtl number < 1, the capacity of heat diffusion is greater than that of momentum diffusion. It is to be observed that all the temperature profiles first enhance a little and then reduce rapidly, which indicates the thermal retardation of Maxwell fluid. Originality/value The unsteady stagnation-point flow model of Maxwell fluid is extended from integral derivative to fractional derivative, which has more flexibility to describe viscoelastic fluid’s complex dynamic process and provide a theoretical basis for industrial processing.

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“…A study of helical flows of generalized Oldroyd-B fluid in porous media with heat transfer was carried out by Li et al 41 They discussed the influence of fractional parameters on both the velocity and temperature fields. Bai et al 42 investigated the heat and mass transfer of three-dimensional (3D) fractional Maxwell fluid over a stretching sheet, where the heat equation was modified by fractional Fourier's law.…”

mentioning

confidence: 99%

Electro‐osmotic flow of fractional second‐grade fluid with fractional Cattaneo heat flux through a vertical microchannel

Abdellateef¹,

Alshehri

Elmaboud

2021

Heat Trans

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This study investigates the unsteady electro-osmotic flow (EOF) of a fractional second-grade fluid through a vertical microchannel with convection heat transfer. The fractional Cattaneo heat flux model will be used to modify the heat equation. The solutions for the velocity and the temperature have been derived by employing the Laplace and finite Fourier sine transforms and their numerical inverses. The results show that at the beginning of the time period, the fractional parameter postpones the movement of the fluid. Furthermore, the results show that at the high values of retardation time (non-Newtonian case), the required time for the velocity and the flow rate to reach the steady state increases. Moreover, the heat relaxation time reduces the heat transfer until a critical time, and then the effect reverses.

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Flow, heat and mass transfer of three-dimensional fractional Maxwell fluid over a bidirectional stretching plate with fractional Fourier’s law and fractional Fick’s law

Cited by 24 publications

References 39 publications

On the process of filtration of fractional viscoelastic liquid food

On the process of filtration of fractional viscoelastic liquid food

Unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time dependent stretching plate with generalized Fourier’s law

Electro‐osmotic flow of fractional second‐grade fluid with fractional Cattaneo heat flux through a vertical microchannel

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