Onset of convection in the Rayleigh–Bénard flow under non-Boussinesq conditions: an asymptotic approach

The effect of temperature dependent fluid properties on the onset of convection in a horizontal fluid layer heated from below is investigated. Based on asymptotic expansions of all fluid properties with respect to temperature final results are deduced that are independent of specific property laws. They are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates. A special point of interest is the widely used Boussinesq approximation. Our asymptotic results clearly show how this approximation affects the stability calculations of the flow under investigation.