Heat transfer optimization for the unsteady mixed convection flow of hybrid nanofluid over a permeable EMHD riga plate with thermal radiation and convective boundary condition

Hybrid nanofluid flow over a Riga plate has broad potential applications in biomedical, chemical, and engineering fields. This study analyzes the mixed convection stagnation-point flow of a hybrid nanofluid over a Riga plate. The effects of thermal radiation, suction, and convective boundary condition are considered by imposing related terms into the governing partial differential equations and boundary conditions. These equations are then reduced into non-linear ordinary differential equations using similarity transformation, and the bvp4c solver in Matlab is used to compute the numerical results. Dual solutions are presented, but only the stable first solution is analyzed and discussed. The presence of suction is found to enhance the magnitude of the local skin friction coefficient, local Nusselt number, and velocity profile of the hybrid nanofluid. However, increasing suction causes the temperature profile to drop. Meanwhile, increasing the nanoparticle volume fraction of Cu and Al2O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Al}_2\hbox {O}_3$$\end{document} in the Al2O3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Al}_2\hbox {O}_3$$\end{document}-Cu/H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}_2$$\end{document}O hybrid nanofluid raises the local skin friction coefficient but reduces the local Nusselt number. In addition, the response surface methodology (RSM) revealed that the suction parameter, Biot number, and radiation parameter favorably impact the local Nusselt number. With desirability of 99.88%, the local Nusselt number is estimated to be maximized at 1.47340 (assisting flow) and 1.47184 (opposing flow) at the highest levels of the suction parameter, Biot number, and radiation parameter (i.e., S=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=0.7$$\end{document}, Bi=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Bi=0.7$$\end{document}, and R=1.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=1.5$$\end{document}).