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采用无量纲格子玻尔兹曼(non-dimensionla lattice Boltzmann method, NDLBM)对方腔内纳米流体的自然对流进行数值模拟, 讨论克努森数($10^{-6} \leqslant Kn_{{\rm{f}},{\rm{s}}} \leqslant 10^4$)、瑞利数($10^3 \leqslant Ra_{{\rm{f}},{\rm{L}}} \leqslant 10^6$)、颗粒体积分数($10^{-2} \leqslant $$ \phi_{\rm{s}} \leqslant 10^{-1}$)等参数对纳米流体流动和传热的影响. 结果表明: 在不同$Ra_{{\rm{f}},{\rm{L}}}$下, 颗粒粒径对传热效率的影响是不同的.在低$Ra_{{\rm{f}},{\rm{L}}}$的热传导区间, 颗粒粒径对传热影响较小; 在高$Ra_{{\rm{f}},{\rm{L}}}$的热对流区间, 较大的颗粒粒径显著提升了流动强度和传热效率. 若保持$Ra_{{\rm{f}},{\rm{L}}}$和$\phi_{\rm{s}}$不变, 随着颗粒粒径的减小, 纳米流体的传热方式由热传导转变为热对流. 此外, 针对高$Ra_{{\rm{f}},{\rm{L}}}$的热对流区间, 在兼顾了导热和流动性的情况下, 最大传热效率所对应的颗粒体积分数为$\phi_{\rm{s}} = 8 {\text{%}}$. 最后, 通过分析平均努塞尔数$\overline {Nu}_{{\rm{f}},{\rm{L}}}$和纳米流体相较于基液增加传热率$Re_{{\rm{n}},{\rm{f}}}$随不同无量纲参数变化的三维等值面图, 发现$\overline {Nu}_{{\rm{f}},{\rm{L}}}$和$Re_{{\rm{n}},{\rm{f}}}$的极值均出现在颗粒粒径为$Kn_{{\rm{f}},{\rm{s}}} = 10^{-1}$. 基于数值结果, 构建$\overline {Nu}_{{\rm{f}},{\rm{L}}}$与$Kn_{{\rm{f}},{\rm{s}}}$、$Ra_{{\rm{f}},{\rm{L}}}$、$\phi_{\rm{s}}$之间的函数关系式, 揭示了这些无量纲参数对传热性能的影响.In this work, numerical simulation of natural convection of nanofluids within a square enclosure were investigated by using the non-dimensional lattice Boltzmann method (NDLBM). The effects of key governing parameters Knudsen number ($10^{-6} \leqslant Kn_{{\rm{f}},{\rm{s}}} \leqslant 10^4$), Rayleigh number ($10^3 \leqslant Ra_{{\rm{f}},{\rm{L}}} \leqslant 10^6$), and nanoparticle volume fraction ($10^{-2} \leqslant \phi_{\rm{s}} \leqslant 10^{-1}$) on the heat and mass transfer of nanofluids were discussed. The results show that in the low $Ra_{{\rm{f}},{\rm{L}}}$ conductive dominated regime, the nanoparticle size has little effect on heat transfer, whereas in the high $Ra_{{\rm{f}},{\rm{L}}}$ convective dominated regime, larger nanoparticle sizes significantly enhance flow intensity and heat transfer efficiency. As fixed $Ra_{{\rm{f}},{\rm{L}}}$ and $\phi_{\rm{s}}$, the heat transfer patterns change from conduction to convection dominated regimes with increasing $Kn_{{\rm{f}},{\rm{s}}}$. The influence of nanoparticle volume fraction was also investigated, and in convection dominated regime, the maximum heat transfer efficiency was achieved when $\phi_{\rm{s}} = 8 {\text{%}}$, balancing both thermal conduction and drag fore of nanofluids. Additionally, by analyzing the full maps of mean Nusselt number ($\overline {Nu}_{{\rm{f}},{\rm{L}}}$) and the enhancement ratio related to the base fluid ($Re_{{\rm{n}},{\rm{f}}}$), the maximum values of $\overline {Nu}_{{\rm{f}},{\rm{L}}}$ and $Re_{{\rm{n}},{\rm{f}}}$ occur when the nanoparticle size is $Kn_{{\rm{f}},{\rm{s}}} = 10^{-1}$ for both conductive and convective dominated regimes. To capture the effects of all key governing parameters on $\overline {Nu}_{{\rm{f}},{\rm{L}}}$, a new empirical correlation has been derived from the numerical results, providing deeper insights into how these parameters influence heat transfer performance.
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ρ/$\mathrm{kg \cdot m^{-3}}$ $c_{p}$/$\mathrm {J \cdot kg^{-1} \cdot K^{-1}}$ k/$\mathrm{W \cdot m^{-1} \cdot K^{-1}}$ λ/$\mathrm{nm}$ 水 997.1 4179 0.613 0.3 ${{\rm{Al}}_2{\rm{O}}_3}$纳米颗粒 3970 765 40 35 
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