Pitfalls in modeling mantle convection with internal heat production

The mantle of the Earth, and probably of other terrestrial planets as well, is heated from below and within. The heating mode of mantle convection is thus mixed heating, and it is also time dependent because the amount of heat-producing isotopes in the mantle is steadily decreasing by radioactive decay and because the basal heat flux originating in the cooling of the core can vary with time. This mode of transient mixed heating presents its own challenges to the study of mantle convection, but such difficulties are not always appreciated in the recent literature. The purpose of this tutorial is to clarify the issue of heating mode by explaining relevant concepts in a coherent manner, including the internal heating ratio, the Urey ratio, secular cooling, and the connection between the thermal budget of the Earth and the geochemical models of the Earth. The importance of such basic concepts will be explained with some illustrative examples in the context of the thermal evolution of the Earth, and a summary of common pitfalls will be provided, with a possible strategy for how to avoid them.