Effects of variable air properties on transient natural convection for large temperature differences

This paper aims to study the effects of air variable properties in the transient case of the classical differentially heated square cavity problem. A SIMPLE algorithm using a low Mach number approximation is applied for coupling the heat and momentum transport equations, which are discretized by the finite volume method. A fully implicit scheme is used for time discretization. The numerical code is validated with benchmark results obtaining a maximum deviation of 0.13% in the average Nusselt number for the non-Boussinesq approach. The temperature and velocity fields as well as the local Nusselt number are numerically studied for Rayleigh numbers ranging between 104 - 107. A temperature difference of 720 K is considered. We have found that the effects of variable properties are especially relevant along the flow development period, amongst which the average Nusselt number, for instance, differs up to roughly 10% with respect to the constant properties case; in contrast, once in steady state regime, such a difference remains less important and is no longer oscillating, resulting around 2%. An investigation is therefore put forward covering additional effects under regard of the principle of energy conservation, such as the time evolution of the total energy and its components for both transient regime and steady state cases. Excepting for the kinetic energy, the internal, potential and total energies are consistently and significantly higher for the case of variable properties; a suitable discussion is provided.