Steady, nonlinear, penetrative convection in a viscous, incompressible fluid confined between free horizontal boundaries in two dimensions is investigated numerically. For Prandtl numbers [sgrave] less than unity and for fixed imposed heat flux, the resulting Rayleigh numberRα [sgrave]−1indicating a strong dependence on the Prandtl number not realised with two-dimensional Rayleigh-Bénard calculations. At low Prandtl numbers, the convection bifurcates supercritically and less efficient heat transport and different cell geometry are exhibited, with no “flywheel” solution in existence.