Stability characteristics of conjugate natural convection boundary layers

Abstract

Flow in a differentially heated two dimensional rectangular cavity, partitioned in the centre by an in finitely conducting vertical wall, has been examined with numerical simulations over Rayleigh numbers around 1010 at Prandtl number 7.5. The configuration is an idealised version of a ow which occurs commonly in engineering settings and is of fundamental importance. Heat is transferred between both sides of the cavity through the conducting wall with natural convection boundary layers forming on all vertical surfaces. We show for the first time that the ow becomes oscillatory above Rayleigh number 1.2 × 1010 for cavity height to width ratio of two, and above Rayleigh number 1.4 × 1010 for cavity height to width ratio of one. The results indicate that the instability is a convective boundary layer instability which becomes absolutely unstable as a result of the thermal coupling across the partition wall. © Austral. Mathematical Soc. 2011.