Abstract
A systematic numerical study of three-dimensional natural convection of air in a differentially heated cubical cavity with Rayleigh number (Ra) up to 1010 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 1010). An exponential scaling law between the Nusselt number and Ra is also found for Ra from 103 to 1010 for the first time, which is also consistent with the available numerical and experimental data at several specific values of Ra.
Highlights
Natural convection flow (NCF) in a differentially heated cubical cavity is one of the fundamental flow configurations in heat transfer and fluid mechanics studies, and it has many significant applications, including air flow in buildings, cooling of electronic devices, and energy storage systems
We find that similar to the temperature field, velocity boundary layers are formed near the isothermal walls, which become thinner with increasing Rayleigh number (Ra), but no apparent velocity boundary layers are developed adjacent to the adiabatic walls
It is found that the maximum difference of Num or Nu0 between the cold and hot walls is less than 0:5%, suggesting that the heat transfer conservation in the cavity is well predicted by the coupled DUGKS (CDUGKS)
Summary
Natural convection flow (NCF) in a differentially heated cubical cavity is one of the fundamental flow configurations in heat transfer and fluid mechanics studies, and it has many significant applications, including air flow in buildings, cooling of electronic devices, and energy storage systems. Different from the NSEs with a nonlinear and nonlocal convection term, the Boltzmann equation is a firstorder linear PDE, and the nonlinearity resides locally in its collision term These features make kinetic methods easy to realize and parallelize with high computational efficiency. Benefiting from the FV nature, non-uniform meshes can be employed without loss of accuracy and additional efforts in DUGKS, and its efficiency can be significantly improved by employing a non-uniform mesh according to the local accuracy requirement [28,29,32] This is the main reason why we use the DUGKS, instead of the LBM, to study the high Rayleigh number natural convection flow, which requires much fine mesh near walls to resolve the thin boundary layers. A scaling correlation between Rayleigh and Nusselt numbers with Ra up to 1010 will be obtained for the first time
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