Thermal and flow dynamics of unsteady MHD nanofluid convection in a partially heated porous cavity

Abstract

This study numerical investigates unsteady freeconvection in a square permeable cavity, driven by magnetohydrodynamic flow of TiO2-H2O nanofluid. The cavity features partially heated vertical walls, with adiabatic bottom and inclined upper walls, a scenario with widespread applications in fields such as heating, ventilation, and air conditioning (HVAC), electronic cooling, solar collectors, building insulation, automotive engineering, geothermal energy, and aerospace technology. The governing equations are discretized using the Marker and Cell (MAC) method, with spatial discretization achieved through the finite difference technique. A staggered grid system is employed to enhance stability and accuracy, and the resulting equations are solved iteratively to capture the unsteady behavior of the system.The study examines the range of Darcy number 10-1 <= Da <= 10-3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {10<^>{ - 1} \le {\text{Da}} \le 10<^>{ - 3} } \right),$$\end{document} Rayleigh number 103 <= Ra <= 106,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {10<^>{3} \le {\text{Ra}} \le 10<^>{6} } \right),$$\end{document} Hartmann number 10 <= Ha <= 30,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {10 \le Ha \le 30} \right),$$\end{document} Prandtl number Pr=6.2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\Pr = 6.2} \right),$$\end{document} inclined magnetic field inclination angle gamma=pi 6,pi 4,pi 3,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\gamma = \frac{\pi }{6},\frac{\pi }{4},\frac{\pi }{3}} \right),$$\end{document} heat source/sink parameter -6 <= Q <= 6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( { - 6 \le Q \le 6} \right)$$\end{document}. Parametric modeling explores, streamline and isotherm plots reveal rising Ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Ra}}$$\end{document} enhance heat transfer, while increased Darcy numbers intensify fluid flow and broaden temperature gradients. Larger heat source/sink parameters expand isotherm contours, amplifying convection. Validation against prior studies confirms the model's reliability and provides insights into the intricate thermal dynamics of the system.