Thermal Creep Flow of Rarefied Gas between Two Parallel Plates

Niimi, Hideyuki

doi:10.1143/jpsj.30.572

Cited by 35 publications

(19 citation statements)

References 5 publications

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“…If we take the limit of κ → 0 (zero curvature limit), problems (55)-(58) reduce to the problems of the Poiseuille flow and thermal transpiration between two parallel plates, which have been widely studied in the literature (e.g. [11,25,19,24,26,36,30,37,31,12]). …”

Section: First Ordermentioning

confidence: 99%

A Diffusion Model for Rarefied Flows in Curved Channels

Aoki¹,

Degond²,

Mieussens³

et al. 2008

Multiscale Model. Simul.

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Abstract. In this paper, we derive a one-dimensional convection-diffusion model for a rarefied gas flow in a two-dimensional curved channel on the basis of the Boltzmann (BGK) model. The flow is driven by the temperature gradient along the channel walls, which is known as the thermal creep phenomenon. This device can be used as a micro-pumping system without any moving part. Our derivation is based on the asymptotic technique of the diffusion approximation. It gives a macroscopic (fluid) approximation of the microscopic (kinetic) equation. We also derive the connection conditions at the junction where the curvature is not continuous. The pumping device is simulated by using a numerical approximation of our convection-diffusion model which turns to agree very well with full two dimensional kinetic simulations. It is then used to obtain very fast computations on long pumping devices, while the computational cost of full kinetic computations is still nowadays prohibitive for such cases.

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Section: First Ordermentioning

confidence: 99%

A Diffusion Model for Rarefied Flows in Curved Channels

Aoki¹,

Degond²,

Mieussens³

et al. 2008

Multiscale Model. Simul.

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“…The thermal transpiration analysis has been carried out for the BKW model [9] as an extension of the thermal creep flow [11]. Our result on the growth of the flow velocity as κ increases is the same as that for the BKW model.…”

Section: Introductionmentioning

confidence: 55%

Thermal transpiration for the linearized Boltzmann equation

Chen

Liu

et al. 2006

Comm Pure Appl Math

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The phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hardsphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation.

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“…14 The relation between Kn and γ has been generally discussed in the literature for two limiting cases: hydrodynamic flow (Kn → 0), and free molecular flow (Kn → ∞). [15][16][17] In the Kn → 0 limit, the heat capacity is already known to be c p = 5k B / 2. As Kn → ∞, γ converges to 0.5, with the deviation from this value decreasing with increasing Knudsen number.…”

Section: Knudsen Heat Capacity For Ideal Gasesmentioning

confidence: 99%

“…For the flow characteristic dependency of the heat capacity, we need a more general relation between Kn and γ that can cover mid-range Knudsen numbers, however, the Kn-γ relations proposed in the literature are not always successful for these systems. [15][16][17] Because of the lack of a welldeveloped analytical expression for the Kn-γ relation over all flow regimes from the hydrodynamic to the free molecular, we have curve-fitted a relationship from data in the literature, 14,18,19 as follows. In Refs.…”

Section: Knudsen Heat Capacity For Ideal Gasesmentioning

confidence: 99%

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Knudsen heat capacity

Babac

Reese

2014

Physics of Fluids

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We present a "Knudsen heat capacity" as a more appropriate and useful fluid property in micro/nanoscale gas systems than the constant pressure heat capacity. At these scales, different fluid processes come to the fore that are not normally observed at the macroscale. For thermodynamic analyses that include these Knudsen processes, using the Knudsen heat capacity can be more effective and physical. We calculate this heat capacity theoretically for non-ideal monatomic and diatomic gases, in particular, helium, nitrogen, and hydrogen. The quantum modification for para and ortho hydrogen is also considered. We numerically model the Knudsen heat capacity using molecular dynamics simulations for the considered gases, and compare these results with the theoretical ones. C ⃝ 2014 AIP Publishing LLC.[http://dx

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Thermal Creep Flow of Rarefied Gas between Two Parallel Plates

Cited by 35 publications

References 5 publications

A Diffusion Model for Rarefied Flows in Curved Channels

A Diffusion Model for Rarefied Flows in Curved Channels

Thermal transpiration for the linearized Boltzmann equation

Knudsen heat capacity

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