A numerical study of the heat transfer through a rarefied gas confined in a microcavity

Rana, Anirudh Singh; Mohammadzadeh, Alireza; Struchtrup, Henning

doi:10.1007/s00161-014-0371-8

Cited by 40 publications

(29 citation statements)

References 28 publications

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“…The simulation results in Refs. [9,10,23] gave good agreement with DSMC and experimental data in internal rarefied gas microflows.…”

Section: Introductionsupporting

confidence: 78%

“…Hadjiconstantinou [10] derived an expression for fully developed slip flow and concluded that the sliding friction (shear work) at the wall should be included to calculate the heat flux from the wall when viscous heat generation needs to be considered. Moreover, the boundary condition of the heat flux of the higher moment method (R-13 equations) proposed by Rana et al [23] also included the slip velocity and stress terms. The simulation results in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Effect of the sliding friction on heat transfer in high-speed rarefied gas flow simulations in CFD

Loc³

2016

International Journal of Thermal Sciences

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“…The simulation results in Refs. [9,10,23] gave good agreement with DSMC and experimental data in internal rarefied gas microflows.…”

Section: Introductionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Effect of the sliding friction on heat transfer in high-speed rarefied gas flow simulations in CFD

Loc³

2016

International Journal of Thermal Sciences

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“…From Eqs. (37), one can obtain the expressions for the stresses and the reduced heat fluxes of the individual components in terms of the other variables. These expressions will be required while obtaining the minimum moments of order O(ε 2 ), and read…”

Section: A Minimum Number Of Moments Of O(ε)mentioning

confidence: 99%

Regularized moment equations for binary gas mixtures: Derivation and linear analysis

2016

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The applicability of the order of magnitude method [H. Struchtrup, “Stable transport equations for rarefied gases at high orders in the Knudsen number,” Phys. Fluids 16, 3921–3934 (2004)] is extended to binary gas mixtures in order to derive various sets of equations—having minimum number of moments at a given order of accuracy in the Knudsen number—for binary mixtures of monatomic-inert-ideal gases interacting with the Maxwell interaction potential. For simplicity, the equations are derived in the linear regime up to third order accuracy in the Knudsen number. At zeroth order, the method produces the Euler equations; at first order, it results into the Fick, Navier–Stokes, and Fourier equations; at second order, it yields a set of 17 moment equations; and at third order, it leads to the regularized 17-moment equations. The transport coefficients in the Fick, Navier–Stokes, and Fourier equations obtained through order of magnitude method are compared with those obtained through the classical Chapman–Enskog expansion method. It is established that the different temperatures of different constituents do not play a role up to second order accurate theories in the Knudsen number, whereas they do contribute to third order accurate theory in the Knudsen number. Furthermore, it is found empirically that the zeroth, first, and second order accurate equations are linearly stable for all binary gas mixtures; however, although the third order accurate regularized 17-moment equations are linearly stable for most of the mixtures, they are linearly unstable for mixtures having extreme difference in molecular masses

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“…All walls except for the driven lid are assumed to be adiabatic; the top wall is fully diffusive and isothermal at T = 273K. The corresponding boundary conditions for a fully diffusive surface in DSMC and R13 equations are well studied and can be found in [34]. This geometry serves as a test for the implementation of the adiabatic boundary conditions (18) for DSMC and (23) …”

Section: A Micro Lid Driven Cavitymentioning

confidence: 99%

DSMC and R13 modeling of the adiabatic surface

Mohammadzadeh

Rana

2016

International Journal of Thermal Sciences

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Adiabatic wall boundary conditions for rarefied gas flows are described with the isotropic scattering model. An appropriate sampling technique for the direct simulation Monte Carlo (DSMC) method is presented, and the corresponding macroscopic boundary equations for the regularized 13-moment system (R13) are obtained. DSMC simulation of a lid driven cavity shows slip at the wall, which, as a viscous effect, creates heat that enters the gas while there is no heat flux in the wall. Analysis with the macroscopic equations and their boundary conditions reveals that this heat flux is due to viscous slip heating, and is the product of slip velocity and shear stress at the adiabatic surface. DSMC simulations of the driven cavity with adiabatic walls are compared to R13 simulations, which both show this non-linear effect in good agreement for Kn < 0.3.

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A numerical study of the heat transfer through a rarefied gas confined in a microcavity

Cited by 40 publications

References 28 publications

Effect of the sliding friction on heat transfer in high-speed rarefied gas flow simulations in CFD

Effect of the sliding friction on heat transfer in high-speed rarefied gas flow simulations in CFD

Regularized moment equations for binary gas mixtures: Derivation and linear analysis

DSMC and R13 modeling of the adiabatic surface

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