Theoretical investigation of steady isothermal slip flow in a curved microchannel with a rectangular cross-section and constant radii of wall curvature

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

doi:10.1016/j.euromechflu.2015.07.002

Cited by 15 publications

(6 citation statements)

References 36 publications

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“…This study resulted in obtaining of velocity and temperature profiles, as well as the Nusselt number, as the functions of the Knudsen, Rayleigh and Prandtl numbers. The results for different fluid flow and heat transfer parameters and functions documented in the works (Avramenko et al, 2015a(Avramenko et al, , 2015b(Avramenko et al, , 2015cAvramenko et al, 2017a) are in a good agreement with analytical solutions. As it was shown in the work (Avramenko et al, 2017b), deviations of the LBM simulations for a circular vertical microchannel from the respective analytical solution is less than 1 per cent for the boundary conditions analogous to those used in the studies (Avramenko et al, 2015a(Avramenko et al, , 2015b(Avramenko et al, , 2015c).…”

Section: Hff 295supporting

confidence: 74%

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Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

Авраменко

Dmitrenko

Shevchuk

et al. 2018

HFF

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Purpose The paper aims to consider heat transfer in incompressible flow in a rotating flat microchannel with allowance for boundary slip conditions of the first and second order. The novelty of the paper encompasses analytical and numerical solutions of the problem, with the latter based on the lattice Boltzmann method (LBM). The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). An increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes a similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which takes into account the second-order boundary conditions. Design/methodology/approach The paper is based on the comparisons of an analytical solution and a numerical solution, which employs the lattice Boltzmann method. Both mathematical approaches used the first-order and second-order slip boundary conditions. The results obtained using both methods agree well with each other. Findings The analytical solution of the problem includes relations for the velocity and temperature profiles and for the Nusselt number depending on the rotation rate of the microchannel and slip velocity. It was demonstrated that the velocity profiles at high rotation rates transform from parabolic to M-shaped with a minimum at the channel axis. The temperature profiles tend to become uniform (i.e. almost constant). The increase in the channel rotation rate contributes to the increase in the Nusselt number. An increase in the Prandtl number causes the similar effect. The trend caused by the effect of the second-order slip boundary conditions depends on the closure hypothesis. It is shown that heat transfer in a flat microchannel can be successfully modeled using the LBM methodology, which considers the second-order boundary conditions. Originality/value The novelty of the paper encompasses analytical and numerical solutions of the problem, whereas the latter are based on the LBM.

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Section: Hff 295supporting

confidence: 74%

“…In the works (Avramenko et al, 2015a(Avramenko et al, , 2015b(Avramenko et al, , 2015c the authors applied the LBM method to simulate steady-state and accelerating flow in straight and curved microchannels. The results for mixed convection in a vertical flat microchannel with slip boundary conditions are presented in Avramenko et al (2017a).…”

Section: Hff 295mentioning

confidence: 99%

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

Авраменко

Dmitrenko

Shevchuk

et al. 2018

HFF

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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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“…По этим причинам механизм переноса массы, импульса и энергии в жидкостях отличается от такового в газах. Теоретические исследования влияния условий проскальзывания при течении газа в микроканалах представлены в работах [4][5][6][7][8][9], где с физической точки зрения влияние проскальзывания на стенке канала описывает число Кнудсена.…”

Section: тепло-та масообмінні процесиunclassified

“…где l -длина проскальзывания воздушной прослойки на стенках канала и задается уравнением (5). Коэффициент аккомодации σ изменяется в пределах от 0,5 до 1.…”

Section: рис 4 зависимость длины проскальзывания от толщины воздушнunclassified

Estimation of the Slip Length in the Flow of Liquid in Micro-Channels

Kovetska

2018

ihe

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Research review of phenomenon for slip flow in micro and nanocannels is presented in the paper. The analysis of theoretical and experimental data characterizing the slip length is carried out. In slip flow in microchannels the slip length is affected by the contact angle of the liquid with the surface, shear stress, pressure, dissipative heating, the amount and nature of the dissolved gas in the liquid, electrical characteristics, surface roughness. Studies of flow in microchannels with hydrophobic walls, which are based on molecular dynamics, showed that the slip length has order of 20 nm. This is much less than the values observed in the experiment. The introduction of an effective (apparent) slip length suggests the existence of a thin layer of gas bubbles near the hydrophobic surface or liquid layer with low value of viscosity and density. Since the idealized model for the total coverage of a hydrophobic surface by gas bubbles gives, as a rule, overestimated values of the slip length in comparison with experimental ones, some researchers consider the inhomogeneous coating of the wall by gas bubbles. In this case, the effect of a layer with a lower viscosity on the slip length turns out to be weaker.

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Theoretical investigation of steady isothermal slip flow in a curved microchannel with a rectangular cross-section and constant radii of wall curvature

Cited by 15 publications

References 36 publications

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

Heat transfer of incompressible flow in a rotating microchannel with slip boundary conditions of second order

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

Estimation of the Slip Length in the Flow of Liquid in Micro-Channels

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