Numerical modeling of natural convection in horizontal and inclined square cavities filled with nanofluid in the presence of magnetic field

In this paper, we have studied the problem of natural convection in an inclined square cavity filled with a Cu/water nanofluid; this is done under a differentially heated configuration in the presence of a magnetic field which tracks the cavity in its inclination. The dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method of second-order accuracy, where the upwind scheme is employed to discretize the convective terms. It turned out that the developed code requires a numerical validation. To do this, a comparison with previously published numerical and experiments results, as well as with the result of simulations under the COMSOL Multiphysics software was performed. The results thus found express very good agreement with the results of the developed code. Heat transfer and fluid flow are examined for parameters of nanoparticles volume fraction (0%≤ϕ≤20%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$0\% \leq \phi \leq 20\%$\end{document}), Grashof number (103≤Gr≤105\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ 10^{3}\leq Gr\leq 10^{5}$\end{document}, Hartmann number (0≤Ha2≤100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ 0\leq Ha^{2}\leq 100$\end{document}), and the cavity inclination angle (0∘≤γ≤π/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ 0^{\circ}\leq\gamma \leq\pi/2$\end{document}). Thus, it is found that a good enhancement in the heat transfer rate can be obtained by adding copper nanoparticles to the base fluid, as well as the increasing of Grashof number. However, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics.