- Poulikakos, D. and Bejan, A., The fluid dynamics of an attic space,
J. Fluid Mech. (UK), vol. 131
pp. 251 - 69 .
(last updated on 2007/04/08)
Reports a fundamental study of the fluid dynamics inside a triangular (attic-shaped) enclosure with cold upper wall and warm horizontal bottom wall. The study was undertaken in three distinct parts. In the first part, the flow and temperature fields in the cavity are determined theoretically on the basis of an asymptotic analysis valid for shallow spaces (H/L→0, where H and L are the attic height and length). It is shown that in the H/L→0 limit the circulation consists of a single elongated cell driven by the cold upper wall. The net heat transfer in this limit is dominated by pure conduction. In the second part of the study, the transient behaviour of the attic fluid is examined, based on a scaling analysis. The transient phenomenon begins wih the sudden cooling of the upper sloped wall. It is shown that both walls develop thermal and viscous layers whose thicknesses increase towards steady-state values. The criterion for the existence of distinct thermal layers in the steady state is (H/L)1/2RaH1/4>1, where RaH is the Raleigh number based on attic height. The corresponding criterion for distinct viscous wall jets is (H/L)1/2RaH1/4Pr-1/2>1, where Pr is the Prandtl number. The third phase of this study focused on a complete sequence of transient numerical simulations covering the ranges H/L=0.2, 0.4, 1; RaH/Pr=10, 103, 105; Pr=0.72, 6