Transient natural convection in enclosures with application to solar thermal storage tanks

Many previously studied natural convection enclosure problems in the literature have the bounding walls of the enclosure responsible for driving the flow. A number of relevant applications contains sources within the enclosure which drive the fluid flow and heat transfer. The motivation for this work is found in solar thermal storage tanks with immersed coil heat exchangers. The heat exchangers provide a means to charge and discharge the thermal energy in the tank. The enclosure is cylindrical and well insulated. Initially the interior fluid is isothermal and quiescent. At time zero, a step change in the source temperature begins to influence the flow. The final condition is a quiescent isothermal fluid field at the source temperature. The governing time-dependent Navier-Stokes and energy equations for this configuration are solved by a finite element method. Solutions are obtained for 10[sup 3] [le] Ra[sub D] [le] 10[sup 6]. Scale analysis is used to obtain time duration estimates of three distinct heat transfer regimes. The transient heat transfer during these regimes are compared with limiting cases. In this paper correlations are presented for the three regimes.