Non-Boussinesq convection and Low Mach Number equations

Thermal convection is fluid motion caused by buoyancy forces arising due to the density variation in non-uniform temperature field. If only small temperature variations are present then it is typical to use the so-called Boussinesq (or Oberbeck-Boussinesq) approximation of the Navier-Stokes and thermal energy equations to model fluid motion. The major feature of such an approximation is the assumption that fluid properties such as thermal conductivity, viscosity, specific heat remain constant while the density is allowed to vary linearly with temperature only in the term representing buoyancy. Such an approximation leads to an accurate description of convection flows if the temperature difference in the flow domain does not exceed a few degrees. However in many physical and industrial applications such as thermal insulation systems, chemical vapour depostion reactors, atmospheric flows the temperature differences reach tens and hundreds degrees. In such situations all assumptions used to justify the Boussinesq approximation fail and a different more complicated modelling approach is required which accounts for realistic nonlinear fluid properties variations