Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface

Loyalka, Sudarshan K.; Petrellis, N.; Storvick, T. S.

doi:10.1063/1.861293

Cited by 88 publications

(65 citation statements)

References 21 publications

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“…Analyzing the parameter γ behavior it is possible to find in which manner the gaswall interaction differs as a function of the used gases and the used surface material on which the gas collides: it is then possible to extract the accommodation coefficient α (18) . As for the results of Storvick, the Porodnov's results are in good agreement with Loyalka's (19) results.…”

Section: Journal Of Thermal Science and Technologysupporting

confidence: 80%

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

Rojas-Cárdenas

Graur

Perrier

et al. 2012

JTST

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By just applying a temperature difference to a micro-system filled with rarefied gas, it is possible to engender a displacement or a compression of the gas in the temperature gradient direction. This is the Thermal Transpiration phenomenon. In the present work, thermal transpiration has been studied both through an experimental approach, which exploits an original measuring system, and through a numerical approach, which is modeled on the basis of the Shakhov model kinetic equation. In both studies, a circular cross section glass micro-tube is submitted to a temperature gradient. The obtained results for Helium, such as the thermal molecular pressure difference, the thermal molecular pressure ratio and the thermal molecular pressure exponent at the final zero-flow stage, are analyzed in the case of a tube submitted to a temperature difference of 51 K. Finally, the obtained thermal molecular pressure ratio results are also compared to the semi-empirical formulas of Liang (1951) and Takaishi and Sensui (1963). These semi-empirical formulas are still in use nowadays to introduce correction factors for pressure measurements done when the pressure gauge functions at different temperatures in respect to the temperature of the operating gas. For the here working pressure conditions and the used tube dimensions the gas rarefaction conditions go from near free molecular to slip regime.

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Section: Journal Of Thermal Science and Technologysupporting

confidence: 80%

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

Rojas-Cárdenas

Graur

Perrier

et al. 2012

JTST

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Section: Estimation Of the Accommodation Coefficientmentioning

confidence: 99%

“…(21) was obtained numerically by Loyalka et al [42] using a BGK model of the Boltzmann equation, whereas Wakabayashi et al [43] solved the linearized Boltzmann equation and obtained a value of 0.98737. In practice, α has also been shown to depend upon the accommodation coefficient [42,44]. Unfortunately, most of the recent experimental estimates of the accommodation coefficient for silicon microchannels have assumed α is unity in accordance with Maxwell's original analysis (e.g., [17,18]).…”

Section: Estimation Of the Accommodation Coefficientmentioning

confidence: 99%

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Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition

Barber

Emerson

2006

Heat Transfer Engineering

152

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“…This assumption allows us to linearize the BGK kinetic model equation. Then, the dimensionless mass flow rate (13) depends mainly on the rarefaction parameter (14) In order to obtain the dimensionless mass flow rate Q the linearized BGK kinetic model equation subjected Maxwell specular-diffuse boundary condition is solved using the discrete velocity method. This mass flow rate through the channel cross section Q is calculated from the bulk velocity (15) The linearized BGK equation is solved for a large range of the rarefaction parameter ( ) and for accommodation coefficient equal to , , and the values of dimensionless mass flow rate is so obtained as a function of the rarefaction parameter.…”

Section: Iv2 Transition and Free Molecular Regimementioning

confidence: 99%

Mass flow measurement through rectangular microchannel from hydrodynamic to near free molecular regimes

2011

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aBSTracT. -The mass flow rate through microchannels with rectangular cross section is measured for a wide Knudsen number range (0.0025-26.2) in isothermal steady conditions. The experimental technique called 'constant Volume Method' is used for the measurements. This method consists of measuring the small pressure variations in the tanks upstream and downstream of the microchannel. The measurements of the mass flow rate are carried out for three gases (Helium, Nitrogen and argon). The microchannel internal surfaces are covered with a thin gold coat of mean roughness characterized by ra = 0.87nm (rMS). The continuum approach (Navier-Stokes equations), associated to the first order velocity slip boundary condition, was used in the slip regime (Knudsen number varies from 0.0025 to 0.1). The experimental velocity slip and the accommodation coefficients based on the Maxwell kinetic boundary condition were deduced. In the transitional and near free molecular regimes the linearized kinetic BGK model was used to calculate numerically the mass flow rate. From the comparison of the numerical and measured values of the mass flow rate the accommodation coefficient was also obtained.Key-words : gas flows, mass flow rate, pressure measurements, accommodation coefficients.

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Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface

Cited by 88 publications

References 21 publications

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

An Experimental and Numerical Study of the Final Zero-Flow Thermal Transpiration Stage

Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition

Mass flow measurement through rectangular microchannel from hydrodynamic to near free molecular regimes

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