In most cases, free convection flows are unstable and hence
transient. Of significant interest is the possibility of a resonance
between the time-dependent forcing function (e.g. time-dependent
power source) and natural frequencies of the system, which can cause
significant amplification of heat transfer rates, above and beyond
the ones caused by either the forcing function
or the natural oscillations.
One of the fundamental models used to study the effects of resonance in free
convection is a rectangular cavity. The top and bottom walls are insulated, the
left wall is kept at a constant temperature, Tc, and at the right
wall either the periodic heat flux, qH(t), or the temperature,
TH(t), is applied. Following Kwak and Hyun (2000), we define
qH(t) = q[1+e
sign (sin ft)] and TH(t) = T
h + DT
e sin ft, where
e is the amplitude of the
forcing function, DT
= Th – Tc , Th is the mean value T
on the right (hot) wall.
The impact of periodic heating is assessed using the following function:
A(f) = [max (
f) – min (
which measures the magnitude of oscillations relative to the non-oscillating value.
We will use the Nusselt number at the vertical center plane, as
the function f. Figure 1 shows a snapshot
of the free convection flow in a cavity with differently heated
walls. Figure 2 shows A(Nu) as a function of the forcing frequency f
normalized by the Brunt-Vaisala frequency, N = (ag DT/H)0.5, where H is the linear size
of the cavity. The figure results were computed using Coolit and
compared to results from Kwak and Hyun (2000).
HS Kwak and JM Hyun, JSME International J., Series B, V. 13, N4,
pp. 532-7, 2000.