We studied the influence of the inhomogeneous boundary conditions on the convection pattern and the response of the pattern to the change of these conditions. These are the idealized models for drifting continental tectospheres at the surface of the Earth. Continental tectosphere acts as a thermal insulator and it can regulate convection upwelling region to come below it. We investigated the transition time of convection patterns and found out that it is much longer than the flow circulation time under some conditions. The Earth satisfies this condition at present
hence we can explain the time scales for aggregation and breakup of continents.