Magnetic mixed convection within wavy trapezoidal thermal energy storage systems using nano enhanced phase change material

The three-dimensional (3D) MHD mixed convection mode confined 3D wavy trapezoidal enclosure is examined. The bottom plane of the trapezoidal system is irregular, particularly a wavy plane with various undulation numbers \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:N$$\end{document}. The forced convection phenomenon arises due to the displacement of the top region plane, whereas the porosity-enthalpy methodology characterizes the progression of charging. The heat transfer is enhanced using the nanoencapsulation phase change material (NePCM), consisting of Polyurethane as a shell and Nonadecane as a core, with water as the primary liquid base. The (GFEM) is used to treat the governing system, and a comparison between the HT (heat transmission) irreversibility and FF (fluid friction) irreversibility is performed using the function of the BeAvg. The significant findings revealed that parabolic behaviors for the melting ribbon curve are given at lower values of Re and higher values of Ha. Also, reducing the undulation number is better for obtaining a higher heat transmission rate. The average Nusselt number was lowered by 60% and 19%, respectively, at the highest Reynolds number when the Hartmann number increased from 0 to 100 and N from 2 to 8. Also, the values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:Re$$\end{document} between 1 and 100 improve the heat transfer rates up to 51%.