Natural convection in thermally stratified enclosures with localized heating from below

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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.