Numerical investigation of electrohydrodynamic solid-liquid phase change in square enclosure

Melting of the dielectric phase change material inside a closed square enclosure is numerically investigated. The fully coupled equations including Navier-Stokes equations, Poisson's equation, charge conservation equation and energy are solved using lattice Boltzmann method (LBM). Strong injection from high temperature vertical electrode considered basic characteristics fluid flow, transport heat transfer in solid-liquid process under coupling Coulomb force buoyancy systematically studied. Emphasis put on analysing influence multiple non-dimensional parameters, electric Rayleigh number <i>T</i>, Stefan <inline-formula><tex-math id="M7">\begin{document}$Ste$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20202127_M7.jpg"/><graphic xlink:href="14-20202127_M7.png"/></alternatives></inline-formula>, mobility <i>M</i>, Prandtl id="M8">\begin{document}$Pr$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M8.jpg"/><graphic xlink:href="14-20202127_M8.png"/></alternatives></inline-formula> electrohydrodynamic (EHD) change. numerical results show that comparing with melting driven by force, applied field will not only flow structure liquid region evolution liquid-solid interface, but also increase efficiency thus enhance process. In particular, we find this phenomenon becomes more pronounced when <i>T</i> larger. Further, dimensionless parameter id="M9">\begin{document}$\varPhi$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M9.jpg"/><graphic xlink:href="14-20202127_M9.png"/></alternatives></inline-formula> introduced to characterize effect EHD enhanced change, indicate enhancement weakened id="M10">\begin{document}$Ste$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M10.jpg"/><graphic xlink:href="14-20202127_M10.png"/></alternatives></inline-formula>, However id="M11">\begin{document}$Ste$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M11.jpg"/><graphic xlink:href="14-20202127_M11.png"/></alternatives></inline-formula> does make much difference for sufficiently it attributed developed convection cells at very early stage Moreover, found negatively related <i>M</i> id="M12">\begin{document}$Pr$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M12.jpg"/><graphic xlink:href="14-20202127_M12.png"/></alternatives></inline-formula> largely depends which due simultaneous force. general, has significant material, especially <i>T</i>,<inline-formula><tex-math id="M13">\begin{document}$Pr$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M13.jpg"/><graphic xlink:href="14-20202127_M13.png"/></alternatives></inline-formula> low id="M14">\begin{document}$Ste$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M14.jpg"/><graphic xlink:href="14-20202127_M14.png"/></alternatives></inline-formula>, <i>M</i>. And quantitatively, all tested cases, maximum time saves about 86.6% id="M15">\begin{document}$T=1000$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M15.jpg"/><graphic xlink:href="14-20202127_M15.png"/></alternatives></inline-formula>, id="M16">\begin{document}$Ra=10000$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M16.jpg"/><graphic xlink:href="14-20202127_M16.png"/></alternatives></inline-formula>, id="M17">\begin{document}$M=3$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M17.jpg"/><graphic xlink:href="14-20202127_M17.png"/></alternatives></inline-formula>, id="M18">\begin{document}$Pr=20$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M18.jpg"/><graphic xlink:href="14-20202127_M18.png"/></alternatives></inline-formula>, id="M19">\begin{document}$Ste=0.1$\end{document}</tex-math><alternatives><graphic xlink:href="14-20202127_M19.jpg"/><graphic xlink:href="14-20202127_M19.png"/></alternatives></inline-formula>.