Natural convection in thermally stratified enclosures with localized heating from below

Abstract

Natural convection flows induced by localized heating of the base of a thermally stratified enclosure are examined. The enclosure is a vertical circular cylinder with height equal to radius. The wall temperature increases linearly with height, and a small heat source is centrally located on the floor. Parameters of the problem are the ambient stratification rate (Γ −1 ), the Prandtl number ( Pr ), and a Grashof number ( Gr ) based on the temperature and the diameter of the heated spot. Over wide ranges of Γ and Gr , vertically layered convection cells are observed in the upper part of the enclosure in both laboratory experiments and numerical calculations. For the case of strong buoyancy and weak stratification, plume-like flows exist immediately above the heat source. Streak photographs are in qualitative accord with the numerical calculations, except for a range of Gr when an azimuthal rotation of the laboratory plume is observed. All flows are otherwise laminar. The theoretical results reveal a √Gr scaling at large Gr for the velocities and heat transfer rates, and a correlation of strongly stratified, viscous flows with the group Gr Pr Γ −1 .