On the thermal evolution of the earth

The two principal contributions to the surface heat flow of the earth are the cooling of the earth and the heat production of radioactive isotopes. As the rate of heat production decreases with time the temperature of the interior of the earth also decreases. The rate of decrease is determined by the ability of solid-state mantle convection to transport the heat to the surface. The dominant effect is the exponential temperature dependence of the mantle viscosity. The non-dimensional mantle temperature can be parameterised in terms of the Rayleigh number for mantle convection. It is found that the mantle is currently cooling at a rate of 36°K/10⁹ years and that three billion years ago the mean temperature was 150°K higher than it is today; 83% of the present surface heat flow is attributed to the decay of radioactive isotopes and 17% to the cooling of the earth. The corresponding mean concentration of uranium in the mantle is 32 ppb.