Natural convection in a cavity with time-varying thermal forcing on a sidewall

Transient natural convection flow is investigated in a two-dimensional square enclosure, subjected to periodic heating and cooling on one sidewall. The thermal forcing applied on the heated sidewall varies with time as a sine wave around a zero mean at a frequency f , with all other walls adiabatic. The time- varying heating/cooling produces an alternating direction vertical natural convection boundary layer that entrains fluid from the cavity interior and discharges it alternatively at the top and bottom of the cavity. The behaviour of the flow is governed by three characteristic time scales, the forcing period, 1/ f , the development time for the boundary layer and the filling time of the cavity. For low forcing frequency the filling time is less than the forcing period and the time average stratification S is well approximated by S ∼f 4 / 5 . For high forcing frequency the forcing period is smaller than the boundary layer development time and S ∼f −2 . The maximum S occurs in a transition region, between the low and high frequency ranges. The maximum value of S increases with increasing Rayleigh number, approaching S ∼= 1 . 0 for the highest values of Rayleigh number considered