Role of nanoparticle radius for heat transfer optimization in MHD dusty fluid across stretching sheet

This research aims to assess the significance of nanoparticle size on the natural convection magnetohydrodynamic (MHD) boundary layer flow of a dusty nanofluid across a stretching sheet. Dusty fluids are widely used in industries such as manufacturing and construction, particularly in areas like infrastructure development and material processing. They are used in petroleum transportation, gas purification, power plant piping, automotive exhaust systems, and sedimentation operations. In this study, dusty nanofluid is composed of copper nanoparticles suspended in a mixture of C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}H6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_6$$\end{document}O2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}-H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}O (50-50%) with a Prandtl number Pr=3.97\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Pr}=3.97$$\end{document}. The similarity transformations convert the governing partial differential equations (PDEs) into ordinary differential equations (ODEs). These ODEs are then solved numerically using MATLAB's built-in "bvp4c" method. The effects of various involved parameters on velocity, temperature, skin friction, and Nusselt number are exemplified graphically. The findings indicate that increasing the nanoparticle radius causes temperatures to decrease for both phases, while increasing velocities for both phases. A rise in the suction parameter results in lower temperature and velocity for both phases. A surge in the Biot number significantly raises the temperatures of both phases. Increasing the suction parameter, nanoparticle radius, and Biot number increases the Nusselt number, which optimizes effective heat transfer efficiency by improving thermal conductivity and nanofluid mobility. Skin friction increases for smaller nanoparticles and enhanced suction.