Start-up slip flow in a microchannel with a rectangular cross section

Авраменко, А. А.; Tyrinov, A. I.; Shevchuk, Igor V.

doi:10.1007/s00162-015-0361-x

Cited by 22 publications

(9 citation statements)

References 44 publications

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“…As has been remarked by Avramenko et al [12], the velocity slip is larger along the longer walls (i.e.,ŷ = ±1). This is essentially a result of a larger velocity gradient near these two walls.…”

Section: Poiseuille Flow Through a Rectangular Channelsupporting

confidence: 54%

“…As was remarked by Matthews and Hastie [13] and Avramenko et al [11,12], these analytical solutions are valuable for future studies. For one thing, they can be used as benchmarks for numerical simulations, or to validate computational fluid dynamics (CFD) codes.…”

Section: Introductionmentioning

confidence: 76%

“…Start-up pressure-driven flows with slip in parallel-plate, circular and rectangular channels were examined recently by Avramenko et al. [11,12], who solved the problems by Laplace transform or series solution methods. Our solutions are expressed in a form simpler than theirs.…”

Section: Introductionmentioning

confidence: 99%

“…The boundary conditions areu = ∓b ∂u ∂y at y = ±h,(81)u = ∓b ∂u ∂x at x = ±a. (82)Start-up slip flow through a rectangular channel has also been investigated by Avramenko et al[12]. They considered a pressure gradient that may vary with time in a power-lawmanner.…”

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confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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This paper contains a collection of problems and their analytical solutions for starting flows under the effect of boundary slip in channels of various geometries. The startup flows examined in this work include: (i) plane Couette flow between two plates, (ii) rotary Couette flow between two coaxial cylinders, (iii) Poiseuille flow through a parallel-plate channel, (iv) Poiseuille flow through a rectangular channel, (v) Poiseuille flow through a circular channel, and (iv) Poiseuille flow through an annulus. It is first shown that, using a depletion layer to model the effective slip, the slip length may attain its steady state much faster than the starting flow will do. This supports the use of a constant Navier slip length in the present problems. Transient solutions are derived in the form of eigenfunction expansions, where the eigenvalues are determined, by solving the characteristic equations numerically, as a function of the channel geometry and the slip lengths. From the leading eigenvalue, it is found that the boundary slip will in general lengthen the transient period of a starting flow.

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Section: Poiseuille Flow Through a Rectangular Channelsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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“…The given above analysis of the research activities on fluid flow and heat transfer in microchannels performed over the past few years indicates that studies incorporated different geometries of microchannels, namely circular, flat, rectangular, and triangular, and straight and curved, subject to different boundary and initial conditions. In the works [15][16][17][18], the lattice Boltzmann method (LBM) was successfully applied to simulate stationary and accelerated microflows in straight and curved microchannels. The simulations enabled quantifying the effects of the Rayleigh, Prandtl, and Nusselt numbers, as well as slippage on the flow development in circular, flat, and curved microchannels.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer and hydrodynamics of slip confusor flow under second-order boundary conditions

Авраменко

Dmitrenko

Shevchuk

2020

J Therm Anal Calorim

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The paper focused on an analytical analysis of the main features of heat transfer in incompressible steady-state flow in a microconfusor with account for the second-order slip boundary conditions. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. As a result, novel solutions were obtained for the velocity and temperature profiles, as well as for the friction coefficient and the Nusselt number. These solutions demonstrated that an increase in the Knudsen number leads to a decrease in the Nusselt number. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics. It was also revealed that flow slippage effects on heat transfer weaken with an increase in the Prandtl number.

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Comparison analysis of analytical and lattice Boltzmann methods for simulation of turbulence decay in flows in converging and diverging channels

et al. 2020

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The paper focuses on a study of turbulence decay in flow with streamwise gradient. For the first time, an analytical solution of this problem was obtained based on the k‐ε model of turbulence in one‐dimensional (1D) approximation, as well as on the symmetry properties of the system of differential equations. Lie group technique enabled reducing the problem to a linear differential equation. The analytical solution enabled parametric studies, which are computationally cheap in comparison to CFD based simulations. The lattice Boltzmann method (LBM) in two‐dimensional approximation (2D) was used to validate the analytical results. Large eddy simulation (LES) Smagorinsky approach was used to close the LBM model. Computations revealed that the rate of turbulence decay is significantly different for the cases of positive and negative streamwise pressure gradient. The further comparisons showed that the analytical solution underpredicts the predictions by the numerical methodology, which can be attributed to the simplified problem statement used to derive the closed‐form analytical solution. Comparisons of calculations with experiments revealed that the theoretical models used in the study underpredict the measurements for flows with a positive pressure gradient. Hence it can be concluded that the LBM technique combined with the LES Smagorinsky model requires the further modification.

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Start-up slip flow in a microchannel with a rectangular cross section

Cited by 22 publications

References 44 publications

Starting flow in channels with boundary slip

Starting flow in channels with boundary slip

Heat transfer and hydrodynamics of slip confusor flow under second-order boundary conditions

Comparison analysis of analytical and lattice Boltzmann methods for simulation of turbulence decay in flows in converging and diverging channels

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