A numerical investigation on the influence of nanoadditive shape on the natural convection and entropy generation inside a rectangle-shaped finned concentric annulus filled with boehmite alumina nanofluid using two-phase mixture model

The goal of this work is to numerically study the hydrothermal and entropy generation specifications of boehmite alumina (γ-AlOOH) nanofluid flowing in a finned concentric annulus using the two-phase mixture model. Different shapes for the nanoadditives are examined including cylindrical, brick, blade, platelet and spherical. The impacts of nanoadditive shape and volume concentration (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}, Rayleigh number (Ra)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{Ra}})$$\end{document} and application of fins on the streamlines, isotherms, Nusselt number as well as both the local and global rates of entropy generation due to the heat transfer and fluid friction are examined. The results indicated that the addition of fins and employing a higher Ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Ra}}$$\end{document} and 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} cause a higher average Nusselt number and generation rate of thermal entropy. Moreover, it was found that, except for Ra=103\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Ra}} = 10^{3}$$\end{document}, the generation rate of frictional entropy intensifies by utilizing fins. Moreover, the frictional entropy generation rate was enhanced using a higher Ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Ra}}$$\end{document} and 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}. The results depicted that the impact of fins on the Nusselt number and entropy generation is not varied by the nanoadditive shape and concentration. Furthermore, it was concluded that the best nanoadditive shape is cylindrical and platelet, respectively, based on the first and the second laws of thermodynamics.