Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure

An enclosure filled with blocks made of a microscale porous medium, separated by macrosize pores, can be treated as a bidisperse porous medium (BDPM) enclosure. This study investigates natural convection resonance inside such a BDPM enclosure subjected to time-periodic heat flux at a side wall, with the opposite wall kept isothermal while the top and bottom walls are adiabatic. The BDPM enclosure is made from uniformly spaced, disconnected, square, porous blocks that form the microporous medium saturated with a fluid of $Pr=0.7$⁠. For Rayleigh numbers, $Ra=108$ and $107$⁠, the pulsating wall heat flux is varied over a frequency range of $0.01≤f≤0.1$⁠, and the bidispersion effect is induced by varying both the internal (micropore) Darcy number $(DaI)$ and external (macropore) Darcy number $DaE$⁠. Natural convection resonance is observed in the BDPM enclosure and the resonance heating frequency $fr$ increases with Ra, $DaI$⁠, and $DaE$⁠. However, $fr$ of the BDPM enclosure is always less than that of the corresponding clear fluid enclosure limit (at $DaI→∞$⁠). Predictions of $fr$ using a modified scale analysis incorporating BDPM effects agree well with that arrived by numerical methods.