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

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Abstract

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 $Ra$.
LanguageEnglish
Pages217-228
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Volume113
Early online date27 May 2017
DOIs
Publication statusE-pub ahead of print - 27 May 2017

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Rayleigh number
Natural convection
free convection
Boundary layers
Kinetic theory of gases
cavities
Scaling laws
boundary layers
Nusselt number
Heat transfer
scaling laws
convection
Air
heat transfer
air
kinetics
gases
Temperature
temperature
Convection

Keywords

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

Cite this

@article{3254c9e03498492eabc27845852c4301,
title = "Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers",
abstract = "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 $Ra$.",
keywords = "three–dimensional natural convection, discrete unified gas–kinetic scheme, heat transfer, flow characteristic, Nusselt number–Rayleigh number correlation",
author = "Peng Wang and Yonghao Zhang and Zhaoli Guo",
year = "2017",
month = "5",
day = "27",
doi = "10.1016/j.ijheatmasstransfer.2017.05.057",
language = "English",
volume = "113",
pages = "217--228",
journal = "International Journal of Heat and Mass Transfer",
issn = "0017-9310",

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TY - JOUR

T1 - Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers

AU - Wang, Peng

AU - Zhang, Yonghao

AU - Guo, Zhaoli

PY - 2017/5/27

Y1 - 2017/5/27

N2 - 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 $Ra$.

AB - 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 $Ra$.

KW - three–dimensional natural convection

KW - discrete unified gas–kinetic scheme

KW - heat transfer

KW - flow characteristic

KW - Nusselt number–Rayleigh number correlation

UR - http://www.sciencedirect.com/science/journal/00179310

U2 - 10.1016/j.ijheatmasstransfer.2017.05.057

DO - 10.1016/j.ijheatmasstransfer.2017.05.057

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JO - International Journal of Heat and Mass Transfer

T2 - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

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