Artificial neural network validation of MHD natural bioconvection in a square enclosure: entropic analysis and optimization

This study numerically investigates inclined magneto-hydrodynamic natural convection in a porous cavity filled with nanofluid containing gyrotactic microorganisms. The governing equations are nondimensionalized and solved using the finite volume method. The simulations examine the impact of key parameters such as heat source length and position, Peclet number, porosity, and heat generation/absorption on flow patterns, temperature distribution, concentration profiles, and microorganism rotation. Results indicate that extending the heat source length enhances convective currents and heat transfer efficiency, while optimizing the heat source position reduces entropy generation. Higher Peclet numbers amplify convective currents and microorganism distribution complexity. Variations in porosity and heat generation/absorption significantly influence flow dynamics. Additionally, the artificial neural network model reliably predicts the mean Nusselt and Sherwood numbers (Nu<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{Nu}$$\end{document} & Sh<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{Sh}$$\end{document}), demonstrating its effectiveness for such analyses. The simulation results reveal that increasing the heat source length significantly enhances heat transfer, as evidenced by a 15% increase in the mean Nusselt number. (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic)(sic) (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic),Peclet(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)/(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic),(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic) (sic). (sic)(sic)(sic)Peclet(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)/(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic) (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic) (Nu<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{Nu}$$\end{document} & Sh<overline>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{Sh}$$\end{document}), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic). (sic)(sic)(sic)(sic)(sic)(sic), (sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic)(sic) (sic)(sic)(sic), (sic)(sic)Nusselt(sic)(sic)(sic)(sic)15%.