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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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