The resonance of natural convection in an enclosure heated periodically from the side

This is a numerical and theoretical investigation of natural convection in a two-dimensional square enclosure with one side cold and isothermal, and the other side heated with pulsating heat flux. It is shown numerically that the buoyancy induced circulation resonates to a certain (single) frequency of the pulsating heat input. The resonance is characterized by maximum fluctuations in the total heat transfer rate through the vertical midplane of the cavity. The numerical experiments cover the Prandtl number range 0.01–7, the heat flux Rayleigh number range 103–109, and the nondimensional frequency range 0– 0.3. It is shown that the critical frequencies determined numerically can be anticipated based on theoretical grounds, by matching the period of the pulsating heat input to the period of the rotation (circulation) of the enclosed fluid. In the last section, the same theoretical argument is used to predict the critical period for natural convection resonance in an enclosed porous medium saturated with fluid.