Numerical study of convection near the stability threshold in a square box with internal heat generation

The Letter presents a numerical study of convection in a finite fluid layer heated from below and with homogeneous internal heat generation. Transitions between the conducting state, hexagonal, and roll flows are investigated for the Prandtl number in the range [0.1,100] and the Rayleigh number from subcritical values up to 1.5Racr. The calculations reveal different directions of circulation in the stable hexagons above and below a critical Prandtl number value Prcr. Close to the Prcr, stable overcritical rolls are detected.