Heatup of an initially isothermal fluid in an enclosure with semi-conducting boundaries

Abstract

The transient buoyant convective process of an initially isothermal fluid in a closed vertical cylinder for large Rayleigh numbers is studied. The thermal forcing is impressed on the interior fluid, through the finitely conducting vetical sidewall, by a sudden increase in the ambient temperature. The idealized theoretical model due to Rahm for one-dimensional temperature evolution in the core is briefly recounted. Finite-difference numerical solutions to the time-dependent Navier-Stokes equations are acquired. These solutions are qualitatively consistent with the physical picture proposed by Rahm. The transient phase of the core temperature field is divided into a stratified region and an isothermal region by a propagating temperature front. The fluid pumping mechanism by the vertical sidewall boundary layer drives a counterclockwise meridional circulation. The global adjustment process is accomplished over the characteristic time scale derived by Rahm. The difficulties and applicability of the theoretical model are examined.