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基于格子玻尔兹曼方法（lattice Boltzmann method, LBM）对磁场作用下纳米流体的自然对流进行数值模拟，系统研究了磁场强度、倾角、颗粒尺寸、颗粒体积分数及瑞利数等参数对热传递过程的影响.研究表明，在颗粒尺寸为Knf = 10-1时，无论处在以热传导或热对流为主的区间，传热效率均达到最大值，表明存在最佳颗粒尺寸以兼顾热物性与粘度平衡. 在低瑞利数区域，磁场对热传递效率的抑制作用较小，而在高瑞利数区，磁场增强了洛伦兹力对流体流动的抑制作用，显著降低了热传递效率. 此外，当磁场倾角为π/2时，洛伦兹力力与浮升力同向协同作用，导致腔内流动强度和传热效率均达到最大. 研究还发现，瑞利数是影响流动强度和温度分布的关键参数，增大瑞利数显著提升对流换热，而颗粒体积分数对导热性的提升作用相对有限. 最后，基于这些数值结果，本文进一步构建了平均努塞尔数与关键无量纲参数之间的经验关联式，定量揭示了各参数对传热性能的影响规律.The lattice Boltzmann method (LBM) was used to simulate natural convection of nanofluids in a square enclosure under the influence of a magnetic field. The research systematically investigates the effects of key parameters, magnetic field strength, tilt angle, nanoparticle size, nanoparticle volume fraction, and Rayleigh number on both heat transfer and fluid flow behaviors. A parametric study was conducted over a wide range of Hartmann numbers (10-6 ≤ Haf,L ≤ 104), magnetic field inclination angles (0 ≤ γB ≤ π), nanoparticle sizes (10-6 ≤ Knf ≤ 104), nanoparticle volume fractions (10-2 ≤ φs ≤ 10-1), and Rayleigh numbers (103 ≤ Raf,L ≤ 106). The results show that when the particle size is Knf = 10-1, the heat transfer efficiency reaches its maximum value regardless of whether heat conduction or convection dominates, indicating the existence of an optimal particle size that balances thermal properties and viscosity. In the low Rayleigh number conduction dominated regime, variations in magnetic field strength have little effect on heat transfer. However, in the high Rayleigh number convection dominated regime, stronger magnetic fields enhance the Lorentz force, which suppresses buoyancy driven flow and reduces heat transfer. The study also demonstrates that the magnetic field tilt angle significantly affects the interaction between the buoyancy force and the Lorentz force. At a tilt angle of π/2, where these forces align, the fluid flow and heat transfer efficiency reach their maximum. Furthermore, the Rayleigh number is identified as a dominant factor in heat transfer, with increasing Rayleigh numbers significantly improving convective heat transfer. The influence of nanoparticle volume fraction on thermal conductivity is less pronounced, yielding only marginal improvements. Finally, the study develops an empirical correlation for the mean Nusselt number as a function of key dimensionless parameters, quantitatively revealing the impact of various factors on heat transfer performance in nanofluids.
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Keywords:
- Magnetic field /
- nanoparticle size /
- nanofluids /
- natural convection /
- lattice Boltzmann method
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