Natural convection in a porous cavity saturated with a non-Newtonian fluid

A numerical and theoretical study is performed to analyze the steady-state natural convection fluid flow and heat transfer in a rectangular porous cavity filled with a non-Newtonian fluid and bounded by impermeable surfaces. The flow is modeled by utilizing the modified Darcy equations. Isothermal boundary conditions are considered where two opposite vertical walls are kept at constant but different temperatures, and the horizontal walls are insulated. The external parameters are the AR, /?«, and powerlaw index. Employing pure scaling arguments, four heat transfer modes are identified: 1) pure conduction, 2) high-/ta convection, 3) distinct horizontal boundary-layer convection, and 4) distinct vertical boundarylayer convection. The results obtained from the scaling arguments are verified numerically. The agreement between the results obtained from the scaling arguments and the numerical model is good. The numerical results are presented in terms of theoretical streamlines and isotherms, the average Nu at the hot wall, the horizontal velocity at the vertical midplane, the vertical velocity at the horizontal midplane, and the temperature distribution at the horizontal and the vertical midplanes.