We propose a modi…cation of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven ‡ows of viscous, incompressible ‡uids. This modi…cation is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous heating cannot be neglected. A simple model problem leads to a coupled system of two parabolic equations...

Similarity transforms of the Boussinesq equation in a semi-in®nite medium are available when the boundary conditions are a power of time. The Boussinesq equation is reduced from a partial di€erential equation to a boundary-value problem. Chen et al. [Trans Porous Media 1995;18:15±36] use a hodograph method to derive an integral equation formulation of the new di€erential equation which they sol...

We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra=2× 10. Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the logNu–logRa slope saturates at a value close to 1/3, as ...

We study the effects of severe non-Boussinesq conditions on thermal convection at the moderate Rayleigh numbers of Ra = 2× 108 and 2× 109 by resorting to direct numerical computations of the full governing equations. We illustrate the effects by considering low temperature gaseous helium. The properties of helium are allowed to depend on the temperature around the mean of 5.4K. The Nusselt numb...

The low-density gas jet injected into a high-density ambient has particular interest in several industrial applications such as fuel leaks, engine exhaust, diffusion flames, materials processing, as well as natural phenomena such fires and volcanic eruptions. The most interesting application of this problem nowaday is the hydrogen leaks in air; since when it mixes with air, fire or explosion ca...

8 We present a new collocated numerical scheme for the approximation of the Navier9 Stokes and energy equations under the Boussinesq assumption for general grids, 10 using the velocity-pressure unknowns. This scheme is based on a recent scheme for 11 the diffusion terms. Stability properties are drawn from particular choices for the 12 pressure gradient and the non-linear terms. Numerical resul...