Non-Boussinesq convection at moderate Rayleigh number in low temperature gaseous helium

We study the effects of severe non-Boussinesq conditions on thermal convection at the moderate Rayleigh numbers of Ra=2×10^8 and 2×10^9 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 5.4 K. The Nusselt number is shown to decrease as the system departs from the Boussinesq approximation. For the Rayleigh numbers chosen here, the role of viscosity in thermal convection is limited to smudging the plume generation at the bottom surface, whereas the thermal expansion coefficient is demonstrated to have a larger impact on heat transport.