Numerical Study of High Gradient Thermobuoyant Flow in a Tilted Cavity Using a Novel Non-Boussinesq Algorithm

Abstract

We study the natural convection heat transfer in a tilted square cavity with different tilt angles. The cavity is subject to a high gradient temperature resulting in high Rayleigh number flows. The fluid is air and is treated as an ideal gas. The flow is laminar. The fluid properties change with temperature variation using Sutherland's law. Because of imposing large temperature gradients to the two cavity opposite walls, there is substantial density variation in the domain. We use a novel non-Boussinesq algorithm to model the density variation fully. Therefore, the current results are considerably different from those obtained using the classical Boussinesq-based methods, which replace the density variation with the temperature changes. The differences become serious as the Rayleigh number increases. The outcome of this study emphasizes that the numerical heat transfer researchers should simulate high thermobuoyant flow domains via applying variable density-based algorithms instead of using the classical Boussinesq-based methods.