Numerical study of two-phase flow in a square cavity under magnetic field of parallel wires

In this paper, a two-phase model is administered to investigate natural convection of Fe3O4–water ferrofluid in a square cavity and under turbulent regime. Ferrofluid flow is exposed to magnetic fields which are induced by two parallel current-carrying wires. The left and right walls of the cavity are maintained at constant temperatures of Th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{h}$$\end{document} and Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{c}$$\end{document} respectively, while the other walls are insulated. In this study, Buongiorno’s two-phase model is modified for considering the nanoparticle diffusion via turbulent eddies and magnetophoresis effects. The Reynolds-averaged Navier–Stokes equations are treated based on v2–f model and the governing equations are solved by the SIMPLE-based finite volume method. The computations are performed for various Rayleigh numbers (107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{7}$$\end{document}, 5×107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5\times 10^{7}$$\end{document} and 108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{8}$$\end{document}), nanoparticle's volume fraction (0≤ϕm≤0.06\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le {\phi }_{m}\le 0.06$$\end{document}) and magnetic numbers ranging from 0 to 3.4×1011\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3.4 \times {10}^{11}$$\end{document}. Numerical results indicate that heat transfer rate and turbulence intensity can be significantly enhanced by the applied magnetic fields. However, the effect of employed magnetic field on heat transfer increment is more pronounced at low Rayleigh numbers.