Nusselt number influenced by expansion/compression, birth/death, and recirculating direction of vortices in elongated enclosures
Abstract 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.
In this paper, we consider the density-dependent incompressible Navier–Stokes equations in with linearly growing initial velocity at infinity. We obtain a blow-up criterion and global well-posedness of the two-dimensional system. It generalized the local well-posedness results due to the recent work by the first and third authors to the global well-posedness in . Copyright © 2012 John Wiley & Sons, Ltd.