Rayleigh-Bénard convection in a supercritical fluid along its critical isochore in a shallow cavity

B. Shen, P. Zhang

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


We perform a numerical investigation of the Rayleigh-Bénard convection in supercritical nitrogen in a shallow enclosure with an aspect ratio of 4. The transient and steady-state fluid behaviors over a wide range of initial distances to the critical point along the critical isochore are obtained and analyzed in response to modest homogeneous bottom heating. On account of the fluid layer being extremely thin, density stratification is notably excluded from consideration herein, which leads to the dominating role of the Rayleigh criterion in the onset of convection. Following the Boussinesq approximation, we find the power law scaling relationships over five decades of the Rayleigh number (Ra) for various transient quantities including the exponential growth rate of the mean enstrophy in the cavity and the characteristic times of the development of convective motion. The correlation of the Nusselt number versus the Rayleigh number shows asymptotic features at the two ends of the Ra spectrum, which incidentally correspond to different convection patterns. Under the regime of high Ra, the heat transfer through the fluid cavity is enhanced by the turbulent bursts of thermal plumes from the boundary layers. On the other hand, under the regime of low Ra, it is the orderly multicellular flow that moves heat from the bottom of the layer to the top, which includes a transition from a four-cell structure to a six-cell structure with decreasing Ra.

Original languageEnglish
Pages (from-to)7151-7165
Number of pages15
JournalInternational Journal of Heat and Mass Transfer
Issue number23-24
Publication statusPublished - Nov 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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