Departures from the Boussinesq approximation in laminar Benard convection

A two‐dimensional computer program has been used to obtain stability and heat transfer results for flow in an air layer heated from below. The gas is contained in a cavity of aspect ratio 20, with rigid conducting top and bottom walls, and rigid insulating side walls. Steady‐state results are presented for a temperature difference parameter e=βΔT/2 as large as 0.6. Consistent with Busse’s analysis [J. Fluid Mech. 30, 625 (1967)], it is found that the critical Rayleigh number and the Nusselt number correlation depend on e2; furthermore the coefficients for the corrections are given here. For small but non‐Boussinesq values of e, the results are in agreement with the linear theory of Busse and the experimental results of Ahlers [J. Fluid Mech. 98, 137 (1980)].