Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

Wang, Xiaoping; Qi, Haitao; Yu, Bo; Xiong, Zuhong; Xu, Huanying

doi:10.1016/j.cnsns.2017.02.019

Cited by 74 publications

(37 citation statements)

References 48 publications

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“…The model plays an important role in describing the behavior of some non‐Newtonian fluids. The direct problems, ie, initial value problem and initial boundary value problems for the time fractional diffusion equation have been studied extensively in recent years, see for instances, other works …”

Section: Introductionmentioning

confidence: 99%

Identifying initial condition of the Rayleigh‐Stokes problem with random noise

Nguyen

Kirane

et al. 2019

Math Methods in App Sciences

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We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well‐known to be ill‐posed because of the rapid decay of the forward process. We construct a regularized solution using the filter regularization method in the Gaussian random noise. Under some a priori assumptions on the exact solution, we establish the expectation between the exact solution and the regularized solution in the L2 and Hm norms.

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Section: Introductionmentioning

confidence: 99%

Identifying initial condition of the Rayleigh‐Stokes problem with random noise

Nguyen

Kirane

et al. 2019

Math Methods in App Sciences

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“…This involves discretization of the equations into finite difference equations at the grid point (i, j). The discretized electric potential, momentum and energy equations respectively become [42]…”

Section: Implicit Finite Difference Approachmentioning

confidence: 99%

Theoretical analysis of transient natural convection flow in a vertical microchannel with electrokinetic effect

Oni

Jha

2019

Journal of Taibah University for Science

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In this article, a theoretical analysis is carried out to understand the role of electrokinetic effect on transient natural convection flow in a vertical microchannel. By incorporating the electrokinetic body force and the natural convection term in the classical Navier-Stokes equations, the governing momentum equation for the current investigation is developed and solved analytically using the classical Laplace transform technique. Due to the complexity of solutions obtained in Laplace domain, the Riemann-sum approximation (RSA) technique is used to transform the solutions from Laplace domain to time domain. For accuracy check, the steady-state solution is also computed and compared with the implicit finite difference method and RSA at large time. Results show that skin-friction at the walls as well as the mass-flux can be optimized by careful selection of flow controlling parameters. In addition, it is found that the time required to attain steadystate skin-friction and mass-flux is weakly dependent on EDL size while strongly dependent on Knudsen number.

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“…The stress tensor component τ xy for fractional second‐grade nanofluid model is:

τ_{x y} = μ_{n f} \frac{\partial u}{\partial y} + λ^{α} D_{t}^{α} ((), \frac{\partial u}{\partial y}),

where μ nf denotes the effective viscosity of nanofluid, u indicates the velocity component along x ‐direction, λ is relaxation time, and D t α denotes the Caputo or Caputo–Fabrizio fractional derivatives.…”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

Shen

Chen

2019

Heat Trans

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The Caputo and Caputo-Fabrizio derivative are applied to study a second-grade nanofluid over a vertical plate. A comparative analysis is presented to study the unsteady free convection of a second-grade nanofluid with a new time-space fractional heat conduction. The governing equations with mixed time-space fractional derivatives are non-dimensionalized and solved numerically, and a comparison between the Caputo and the Caputo-Fabrizio models is made. It is found that the temperature is higher for the Caputo-Fabrizio fractional model than the Caputo model, but the higher velocity only exists near the vertical plate for the Caputo-Fabrizio model than the Caputo model. Moreover, the velocity for the Caputo model will exceed the Caputo-Fabrizio model as y evolves. K E Y W O R D SCaputo fractional derivative, Caputo-Fabrizio fractional derivative, heat transfer, second-grade nanofluid | INTRODUCTIONThe second-grade fluid is a popular non-Newtonian fluid, and has been used in petroleum industry, chemical industry, light industry, and many other sectors. The second-grade fluid model was first configured by Coleman and Noll, 1 and the heat transfer of the second-grade fluid under various physical conditions has been investigated widely. [2][3][4][5][6] Fractional derivative is suitable for describing some substantial problems than the regular derivative, and it has been applied widely to establish mathematical models of realistic problems. Fractional calculus has been used to establish the constitutive relations of viscoelastic materials and anomalous diffusions. 7-11 Sin et al 12 introduced the fractional K-BKZ model to viscoelastic fluid for the study of unsteady flow between parallel plates, and the fractional Cattaneo-Christov flux model was used by Liu et al 13 to study the diffusion in comb frame. As the nanofluid has better heat transfer efficiency than conventional fluids, 14 the heat transfer of nanofluid flow under various physical conditions has been investigated. [15][16][17] Shen et al 18 proposed a renovated Buongiorno's model with fractional differential equation to study the heat transfer characteristics of Sisko nanofluid. It is clear to note that the researchers mostly utilized Caputo and Riemann-Liouville derivatives with singular kernels.The Caputo-Fabrizio derivative with an unsingular kernel was given by Caputo and Fabrizio, 19 which was based on the exponential function to eliminate the singular kernel. Ali et al 20 used this derivative to investigate magnetohydrodynamics free convection flow on a static vertical plate for generalized Walters'-B fluid, and Asjad et al 6 studied the feature of Caputo and Caputo-Fabrizio fractional derivatives for an unsteady second-grade fluid with Newtonian heating.In this paper, a new time-space fractional heat conduction is introduced into the energy equation to investigate the heat transfer of second-grade nanofluids on a vertical plate by using Tiwari and Das's model. 21 The Caputo and Caputo-Fabrizio derivatives are applied to get numerical solutions of the d...

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Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids

Cited by 74 publications

References 48 publications

Identifying initial condition of the Rayleigh‐Stokes problem with random noise

Identifying initial condition of the Rayleigh‐Stokes problem with random noise

Theoretical analysis of transient natural convection flow in a vertical microchannel with electrokinetic effect

Unsteady free convection of second‐grade nanofluid with a new time‐space fractional heat conduction

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