The inner core and the surface heat flow as clues to estimating the initial temperature of the Earth's core

This paper attempts to estimate the temperature of the deep interior of the early Earth. The initial temperature cannot be too high or too low in order to realize the present-day thermal state, such as the surface heat flow and the inner core size. Two constraints have been placed: (1) The age of the con is 4.4 X 10(9) years, comprised of periods of liquid phase and liquid-solid phase. (2) the present-day heat flow is 4.3 X 10(13) W at the Earth's surface. Global energy balance equations for a parameterized convection model an solved to obtain the initial temperature that satisfies the constraints. The model includes the effect of the inner core growth as well as partial layering of mantle convection. The effect of the partial layering is taken into the model by assuming enhanced thermal conduction across the mid-mantle transition zone, with conductivity cu, times as high as the background. The parameter beta in the Nusselt-Rayleigh number relationship is also employed as an adjustable parameter. Our preferred model for the mantle with a homogeneous distribution of radioactive elements gives 4200 +/- 80 K as the initial temperature at the core mantle boundary with parameters alpha(K) = 3, beta = 0.1, based on Boehler's model of melting temperature of the core. alpha(K) can be related to partial layering parameter representing the mass flux across the transition zone. alpha(K) = 3 implies about 70% mass flux, in comparison with whole mantle convection, flowing across the transition zone. The initial temperature 4200 K leads to the present-day temperature of 3820 K at the core mantle boundary. Temperature of the thermal boundary layer at the base of the mantle has been estimated to be 2940 K at its the top surface, producing 880 K decrease across the boundary with a thickness of 180 km. Total heat flow from the core to the mantle is obtained to be 7.5 X 10(12) W, while it was 8.0 X 10(12) W when the inner core began to solidify 1.9 X 10(9) years ago. (C) 2000 Elsevier Science B.V. All rights reserved.