NATURAL CONVECTION ABOVE AN ARRAY OF OPEN CAVITIES HEATED FROM BELOW

Abstract

The effect of buoyancy on the flow and heat transfer that develop between a horizontal cold surface and an infinite two-dimensional array of open cavities heated from below is studied numerically. In earlier investigations the steady-state features of this problem were studied for the case of unbounded flow above the cavities. The resulting flow pattern was found to be symmetrical with respect to the centerlines of the cavities. In the present work it is shown that the symmetry of the flow can be destroyed due to the presence of an upper wall. The evolutionary path to steady-state flow is examined, and sustained oscillatory behavior has been observed in several cases. The solution structure is governed by five parameters, i.e., the geometric parameters A = l'/H', B = h'/H', and C = L'/H', the Rayleigh number Ra = gβ ΔT' H' ³/av, and the Prandtl number Pr = v/α. For a geometry with A = ½z, B = ¼, and C = 1, a complicated solution structure is observed upon increasing the Rayleigh number. For Ra ≤ 4 × 10³, a steady symmetric two-cell pattern is observed. This pattern becomes asymmetric for 4 × 10³ < Ra ≤ 9 × 10⁴, periodic for Ra ≤ 3 × 10⁵ and chaotic above that. The transition to periodic convection occurs at lower Rayleigh numbers with decreasing B.