Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers

Peng Wang, Yonghao Zhang, Zhaoli Guo

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A systematic numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number ($Ra$) up to $10^{10}$ is performed by using the recently developed coupled discrete unified gas-kinetic scheme. It is found that temperature and velocity boundary layers are developed adjacent to the isothermal walls, and become thinner as $Ra$ increases, while no apparent boundary layer appears near adiabatic walls. Also, the lateral adiabatic walls apparently suppress the convection in the cavity, however, the effect on overall heat transfer decreases with increasing $Ra$. Moreover, the detailed data of some specific important characteristic quantities is first presented for the cases of high $Ra$ (up to $10^{10}$) . An exponential scaling law between the Nusselt number and $Ra$ is also found for $Ra$ from $10^3$ to $10^{10}$ for the first time, which is also consistent with the available numerical and experimental data at several specific values of $Ra$.
Original languageEnglish
Pages (from-to)217-228
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Early online date27 May 2017
Publication statusE-pub ahead of print - 27 May 2017


  • three–dimensional natural convection
  • discrete unified gas–kinetic scheme
  • heat transfer
  • flow characteristic
  • Nusselt number–Rayleigh number correlation


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