Parameterized convection within the moon and the terrestrial planets

For a fluid layer or a self-gravitating fluid sphere uniformly heated from within, the internal temperature can be parameterized in terms of the appropriate Rayleigh number. The heat generation term includes both radioactive heat release and transient heating or cooling. This parameterization has been verified by comparisons with laboratory experiments. Thermal history calculations have been carried out for the earth, Venus, Mars, Mercury, and the moon. The results for the earth and Venus indicate that two scales of convection are occurring, one including the surface plates and the second occurring beneath the surface plates. In all cases the present heat flows are between seven and twelve per cent greater than the values obtained assuming a steady state balance between heat flow and internal heat generation.