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Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo

Alireza Mohammadzadeh, Ehsan Roohi, and Hamid Niazmand

Stefan Stefanov*

Rho Shin Myong

  • Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, PO Box: 91775-1111, Mashhad, Iran

  • Institute of Mechanics, Bulgarian Academy of Science, Acad. G. Bontchev str., 1113, Sofia, Bulgaria

  • Department of Aerospace and System Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, South Korea

  • *Corresponding author.
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Phys. Rev. E 85, 056310 – Published 23 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.056310

Abstract

In this study the direct-simulation Monte Carlo (DSMC) method is utilized to investigate thermal characteristics of micro- or nanocavity flow. The rarefied cavity flow shows unconventional behaviors which cannot be predicted by the Fourier law, the constitutive relation for the continuum heat transfer. Our analysis in this study confirms some recent observations and shows that the gaseous flow near the top-left corner of the cavity is in a strong nonequilibrium state even within the early slip regime, Kn=0.005. As we obtained slip velocity and temperature jump on the driven lid of the cavity, we reported meaningful discrepancies between the direct and macroscopic sampling of rarefied flow properties in the DSMC method due to existence of nonequilibrium effects in the corners of cavity. The existence of unconventional nonequilibrium heat transfer mechanisms in the middle of slip regime, Kn=0.05, results in the appearance of cold-to-hot heat transfer in the microcavity. In the current study we demonstrate that existence of such unconventional heat transfer is strongly dependent on the Reynolds number and it vanishes in the large values of the lid velocity. As we compared DSMC solution with the results of regularized 13 moments (R13) equations, we showed that the thermal characteristic of the microcavity obtained by the R13 method coincides with the DSMC prediction. Our investigation also includes the analysis of molecular entropy in the microcavity to explain the heat transfer mechanism with the aid of the second law of thermodynamics. To this aim, we obtained the two-dimensional velocity distribution functions to report the molecular-based entropy distribution, and show that the cold-to-hot heat transfer in the cavity is well in accordance with the second law of thermodynamics and takes place in the direction of increasing entropy. At the end we introduce the entropy density for the rarefied flow and show that it can accurately illustrate departure from the equilibrium state.

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Outline

Information

Phys. Rev. E 85, 056310– Published 23 May, 2012
  • Received 11 November 2011
Article part of CHORUS

©2012 American Physical Society

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