The results of numerical simulation of unsteady free convection developing near a suddenly heated plate, on which protrusions in the form of adiabatic cylinders of double height with respect to the diameter are arranged in a checkerboard pattern, are presented. The calculations were performed according to the Reynolds equations using a differential model of turbulent stresses. The range of variation of the Grashof number (plotted according to the thickness of the free convective flow), in which a significant intensification of heat transfer can be achieved, has been determined. It is shown that the best conditions for intensification are created if the longitudinal pitch in the array of protrusions is approximately twenty times the diameter of the latter.