Heat transfer enhancement analysis of mixed convection Cu/CuO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Cu}}/{\text{CuO}}$$\end{document}–water magneto-hybrid nanofluid flow in a square enclosure with hot and cold slits in non-Darcy porous medium

The fluid flow over an extending cavity has many applications in different fields which include manufacturing processes, treatment of various diseases, destruction of cancer tissue, artificial lungs and radiators, heat and mass transfer, biomedical applications, environmental science, and energy production. The heat transfer investigated mixed convection MHD with Cu/CuO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Cu}}/{\text{CuO}}$$\end{document}–water hybrid nanofluid flow in a square cavity with a non-Darcy porous medium. In this study, the MAC (Marker and Cell) technique is to solve the resulting governing non-dimensional partial differential equation within a staggered grid system. The MATLAB®\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\text{MATLAB}}}^{\mathrm{\circledR }}$$\end{document} software is used to obtain the contours of streamlines and isotherms. In comparison with prior research, the average Nusselt number obtained under identical conditions validates the accuracy of the current study’s findings. The impact of magnetic field (Ha)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{Ha}})$$\end{document}, non-Darcy (Da)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{Da}})$$\end{document}, and heat sink/source (Q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Q)$$\end{document} parameters are discussed. The results of the current study assert that the square cavity of heat and energy transfer increases as the non-Darcy parameter value (Da=0.001,0.01,0.1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{Da}} = 0.001, \, 0.01, \, 0.1)$$\end{document} increases. The heat transfer rate is very slow as the Hartmann number (Ha=0,20,40)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{Ha}} = 0, \, 20, \, 40)$$\end{document} increases. Finally, heat transfer increases as the influence of the heat generation/absorption parameter (Q=-6,0,6)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Q=-6, \, 0, \, 6)$$\end{document} also increases.