Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

Wang, Shaowei; Zhao, Moli; Li, Xicheng; Chen, Xi; Ge, Yanhui

doi:10.5560/zna.2014-0066

Cited by 12 publications

(2 citation statements)

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“…The constitutive equation for a fractional second‐grade fluid based on the Riemann‐Liouville fractional‐order derivative 34,44,60 is taken as

τ ((), t) = μ ε (t) + α_{1}^{γ} D_{t}^{γ} ([], μ ε (t)), 0 < γ < 1,

where

ε

denotes the shear strain. The first term of Equation (1) depicts the elastic element and the latter provides the viscous term which includes the fractional‐order (

γ

) derivative with time

t

.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Electroosmotic flow of a fractional second‐grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

Dey

Shit

2020

Heat Trans

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We investigated the time‐dependent viscoelastic fluid flow through a parallel‐plate microchannel under the influence of a transversely applied magnetic field and an axially imposed electric field. We performed the analysis by employing the Poisson‐Boltzmann equation under the Debye‐Huckel approximation. The generalized second‐grade fluid model with a fractional‐order time derivative is used to observe the non‐Newtonian and fractional behavior rates of deformation employing the Riemann‐Liouville fractional operator. We considered the asymmetric zeta potentials and different slip effects at the walls to study the flow behavior near the vicinity of the channel. We obtained an analytical solution in terms of Mittag‐Leffler function, applying Fourier and Laplace transformations. We imposed the heat transfer phenomena with the dissipation of energy and Joule heating effects on the model. The governing equations were also solved numerically by employing an implicit finite difference scheme. The numerical solution was compared with the analytical results, considering the influence of the pertinent parameters involved in the problem. The study delineates that the flow rate decreases with a rise in the fractional‐order parameter, while the opposite trend is observed with the electroosmotic parameter. Due to the application of sufficient strength of the magnetic field and the Joule heating effects, the temperature increases within the channel.

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“…The constitutive equation for a fractional second‐grade fluid based on the Riemann‐Liouville fractional‐order derivative 34,44,60 is taken as

τ ((), t) = μ ε (t) + α_{1}^{γ} D_{t}^{γ} ([], μ ε (t)), 0 < γ < 1,

where

ε

denotes the shear strain. The first term of Equation (1) depicts the elastic element and the latter provides the viscous term which includes the fractional‐order (

γ

) derivative with time

t

.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Electroosmotic flow of a fractional second‐grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

Dey

Shit

2020

Heat Trans

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“…These fluids can not be treated as New- fluid and the modified second grade fluid is the simplest constitutive model that can describe shear-thinning (or shear-thicking) and normal stress differences [46]. It is for this reason that Wang et al [43] studied the electroosmotic flow of biofluid firstly using the generalized second grade fluid with fractional derivative. But to our best knowledge, exact solutions for the electroosmotic flow of viscoelastic fluids are rarely reported yet.…”

mentioning

confidence: 99%

Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

Wang

2017

Can. J. Phys.

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This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

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Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

Alsharif

Abdellateef²,

Elmaboud

et al. 2022

Appl. Math. Mech.-Engl. Ed.

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Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

Cited by 12 publications

References 0 publications

Electroosmotic flow of a fractional second‐grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

Electroosmotic flow of a fractional second‐grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

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