Marginal convection in a large rigid box

The Nusselt number defining the heat transfer across the bottom of a large rectangular box containing fluid whose lower horizontal face is uniformly heated from below, when the Rayleigh number is approximately equal to its critical value for the onset of convection, is calculated. The general method follows that used by Daniels in his study of the same problem, except that he assumed that the horizontal boundaries are stress-free. The simplicity of his approach is lost when the more realistic conditions of rigid boundaries are taken into account and a number of extensive computations are required before the Nusselt number variation can be determined.