Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure

Abstract

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.