Numerical experiments with free convection in a vertical slot

Numerical solutions of the equations of steady free convection in a vertical slot have been obtained by a procedure which relies solely on an iterative solution of Poisson's equation. With a mesh spacing of $\frac{1}{40}$ the solutions are stable up to a Rayleigh number of order 10⁵. The numerical experiments are comparable to the author's laboratory experiments (Elder 1965) and to the experiments of Eckert & Carlson (1961). The growth of the boundary layers and the uniform vertical temperature gradient are well described. It is tentatively suggested that certain unstable motions found prior to the divergence of the numerical solution are comparable to the secondary flows found by the author.