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Richard O’Connell Harvard University Abstract: A recent analytic boundary layer model of convection with layered viscosity and tectonic plates has revealed the existence of multiple convective modes, with transitions and hysteresis. Modes include ‘classical’ plate tectonics, a sluggish plate mode and a foundering plate mode. Analytic results compare well with numerical convection calculations. When applied to the thermal evolution of the Earth the model predicts possible transitions between modes during Earth history, depending on the evolution of lower mantle viscosity. Such models can reconcile the apparent discrepancy between the current terrestrial heat flow and the esitmated concentration of heat sources in the Earth (the Urey ratio). The model allows the efficient investigation of the tectonic and thermal evolution of terrestrial planets and exo-planets.