Lattice Boltzmann method simulated effect of nanoparticle size on natural convection patterns of nanofluids
Authors: Sui Peng-Xiang ,   College of Elementary Education, Capital Normal University, Beijing 100048, China
Published: October 2024

In this work, numerical simulation of natural convection of nanofluids within a square enclosure are conducted by using the non-dimensional lattice Boltzmann method (NDLBM). The effects of key governing parameters Knudsen number (<inline-formula><tex-math id="M20">\begin{document}$10^{-6} \leqslant Kn_{{\rm{f}},{\rm{s}}} \leqslant 10^4$\end{document}</tex-math></inline-formula>), Rayleigh number (<inline-formula><tex-math id="M21">\begin{document}$10^3 \leqslant Ra_{{\rm{f}},{\rm{L}}} \leqslant 10^6$\end{document}</tex-math></inline-formula>), and nanoparticle volume fraction (<inline-formula><tex-math id="M22">\begin{document}$10^{-2} \leqslant \phi_{\rm{s}} \leqslant 10^{-1}$\end{document}</tex-math></inline-formula>) on the heat and mass transfer of nanofluids are discussed. The results show that in the low <inline-formula><tex-math id="M23">\begin{document}$Ra_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula> conduction dominated regime, the nanoparticle size has little effect on heat transfer, whereas in the high <inline-formula><tex-math id="M24">\begin{document}$Ra_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula> convection dominated regime, larger nanoparticle size significantly enhances flow intensity and heat transfer efficiency. For fixed <inline-formula><tex-math id="M25">\begin{document}$Ra_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M26">\begin{document}$\phi_{\rm{s}}$\end{document}</tex-math></inline-formula>, the heat transfer patterns change from conduction to convection dominated regime with <inline-formula><tex-math id="M27">\begin{document}$Kn_{{\rm{f}},{\rm{s}}}$\end{document}</tex-math></inline-formula> increasing. The influence of nanoparticle volume fraction is also investigated, and in the convection-dominated regime, the maximum heat transfer efficiency is achieved when <inline-formula><tex-math id="M28">\begin{document}$\phi_{\rm{s}} = 8 {\text{%}}$\end{document}</tex-math></inline-formula>, balancing thermal conduction and drag fore of nanofluid. Additionally, by analyzing the full maps of mean Nusselt number (<inline-formula><tex-math id="M29">\begin{document}$\overline {Nu}_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula>) and the enhancement ratio related to the base fluid (<inline-formula><tex-math id="M30">\begin{document}$Re_{{\rm{n}},{\rm{f}}}$\end{document}</tex-math></inline-formula>), the maximum value of <inline-formula><tex-math id="M31">\begin{document}$\overline {Nu}_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M32">\begin{document}$Re_{{\rm{n}},{\rm{f}}}$\end{document}</tex-math></inline-formula> occur when the nanoparticle size is <inline-formula><tex-math id="M33">\begin{document}$Kn_{{\rm{f}},{\rm{s}}} = 10^{-1}$\end{document}</tex-math></inline-formula> for both conductive and convection dominated regime. To ascertain the effects of all key governing parameters on <inline-formula><tex-math id="M34">\begin{document}$\overline {Nu}_{{\rm{f}},{\rm{L}}}$\end{document}</tex-math></inline-formula>, a new empirical correlation is derived from the numerical results, providing a more in-depth insight into how these parameters influence on heat transfer performance.