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Research Papers: Heat and Mass Transfer

An Investigation of Heat Transfer in a Cavity Flow in the Noncontinuum Regime

[+] Author and Article Information
Chariton Christou, S. Kokou Dadzie

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 29, 2016; final manuscript received March 10, 2017; published online May 2, 2017. Assoc. Editor: George S. Dulikravich.

J. Heat Transfer 139(9), 092002 (May 02, 2017) (10 pages) Paper No: HT-16-1540; doi: 10.1115/1.4036340 History: Received August 29, 2016; Revised March 10, 2017

Volume diffusion (or bi-velocity) continuum model offers an alternative modification to the standard Navier–Stokes for simulating rarefied gas flows. According to this continuum model, at higher Knudsen numbers the contribution of molecular spatial stochasticity increases. In this paper, we study a microcavity heat transfer problem as it provides an excellent test for new continuum flow equations. Simulations are carried out for Knudsen numbers within the slip and higher transition flow regimes where nonlocal-equilibrium and rarefaction effects dominate. We contrast the predictions by a Navier–Stokes model corrected by volume diffusion flux in its constitutive equations to that of the direct simulation Monte Carlo (DSMC) method and the standard Navier–Stokes model. The results show improvement in the Navier–Stokes prediction for the high Knudsen numbers. The new model exhibits proper Knudsen boundary layer in the temperature and velocity fields.

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Figures

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Fig. 1

Configuration of the microcavity flow problem

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Fig. 2.

Energetic heat flux (a) and entropic heat flux (b) lines overlaid on the temperature contour for Kn = 10 in comparison with DSMC heat flux (c)

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Fig. 3

Variation of gas temperature near the top lid (y/L = 0.9) of the cavity for DSMC, NSF, and volume diffusion at Kn = 10

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Fig. 4

Energetic heat flux (a) and entropic heat flux (b) lines overlaid on the temperature contour for Kn = 1 in comparison with DSMC heat flux (c)

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Fig. 5

Variation of gas temperature near the top lid (y/L = 0.9) of the cavity for DSMC, NSF, and volume diffusion at Kn = 1

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Fig. 6

Energetic heat flux (a) and entropic heat flux (b) lines overlaid on the temperature contour for Kn = 0.1 in comparison with DSMC heat flux (c)

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Fig. 7

Variation of gas temperature near the top lid (y/L = 0.9) of the cavity for DSMC, NSF, and volume diffusion at Kn = 0.1

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Fig. 8

Computed (a) u-velocity profile plotted along a vertical line and (b) v-velocity profile plotted along a horizontal line, crossing the center of the cavity UDSMC, Um, and Uv at Kn = 10

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Fig. 9

Computed (a) u-velocity profile plotted along a vertical line and (b) v-velocity profile plotted along a horizontal line, crossing the center of the cavity UDSMC, Um, and Uv at Kn = 1

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Fig. 10

Computed (a) u-velocity profile plotted along a vertical line and (b) v-velocity profile plotted along a horizontal line, crossing the center of the cavity UDSMC, Um, and Uv for Kn = 0.1

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Fig. 11

Normalized shear stress profiles along the horizontal line of the cavity for (a) Kn = 10, (b) Kn = 1, and (c) Kn = 0.1

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Fig. 12

Temperature variation comparison for three different models: (a) NSF, (b) DSMC, and (c) volume diffusion

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Fig. 13

Knudsen layer thickness at varying Knudsen number

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Fig. 14

Comparison (volume diffusion versus John et al. DSMC) of the normalized temperature profile along the center of the cavity at Kn = 8

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Fig. 15

Comparison of ux component between volume diffusion and Varoutis et al. configuration [34]

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Fig. 16

Energetic heat flux lines overlaid on the temperature contour, argon (a) and (c) and helium (b) and (d); Kn = 0.1 in (a) and (b) and Kn = 1 in (c) and (d)

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Fig. 17

Comparison between DSMC and volume diffusion CPU ratio with respect to Knudsen number

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