Nusselt number influenced by expansion/compression, birth/death, and recirculating direction of vortices in elongated enclosures

Buoyancy-driven recirculating flows between two parallel plates, whose temperature varies sinusoidally, have been attentively investigated. In this study, we place our emphasis on joint effects rendered by both (a) the existence of two insulated side walls and (b) the phase of the bottom-surface sinusoidal temperature on the overall Nusselt number (Nu) of the system. Using the finite-element-based COMSOL and the finite-volume-based ANSYS Fluent packages, we have discovered that Nu is gradually affected by expansion and compression of vortices, as well as is abruptly affected by birth and death of vortices. Under the width-divided-by-height aspect ratio of ten, these gradual or abrupt variations for airflows remain conspicuous regardless of the wave number and the Rayleigh number.