Free convection/radiation and entropy generation analyses for nanofluid of inclined square enclosure with uniform magnetic field

This paper studies the generation of entropy and free convective heat transfer of Al2O3/water nanofluid in an inclined enclosure affected by a magnetic field considering radiation effects. There is a circular quadrant at temperature Th\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\text{h}}$$\end{document} in the bottom section of the left wall of the enclosure. The right wall of enclosure is kept at a fixed temperature Tc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\text{c}}$$\end{document}. The other walls are insulated. The governing equations for fluid flow are resolved using the algorithm of SIMPLE. The effect of variations of Rayleigh number (Ra), Hartmann number (Ha), the enclosure angle and concentration of nanoparticles (φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi$$\end{document}) on the flow field, isothermal field, entropy field, Nusselt number (Nu), Bejan number (Be) and total generation of entropy is investigated. The results indicate that the Nu enhances by 160% and 40% by augmenting the Ra and decreasing the Ha, respectively. Be diminishes by enhancing the Ra and reducing the Ha. The maximum generation of entropy intensifies by 288% and 39% by augmenting the Ra and reducing the Ha, respectively. The highest average Nusselt umber (NuM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Nu}}_{\text{M}}$$\end{document}) and an overall generation of entropy occur at the inclination angle of 30°.