The Gruneisen parameter for iron at outer core conditions and the resulting conductive heat and power in the core

The aim of this paper is to find the conductive power in the outer core. Before the heat conduction equation can be usefully applied, however, a careful examination of the Gruneisen parameter, gamma, and the thermal conductivity, kappa(c), of the core is required. The focus of this paper is on these two parameters at outer core conditions, using primarily experimental data and one theoretical evaluation of gamma. The melting gamma(m) of the core is found to be 1.3, the adiabatic gamma(ad), slightly less, and kappa(c) is found to be 44 W m(-1) K-1 in the upper limit and 28 W m(-1) K-1 in the lower limit. To obtain the core's temperature, T-m, from T-m of pure iron (at core conditions), the freezing point depression is found. This requires assumptions about the impurities in the iron core. Recent experimental data greatly restrict the type and concentrations of these impurities. Several allowable combinations are found, however; all of these lead to a Delta T of similar to 1000 K. At the core side of the core-mantle boundary (CMB), the adiabatic temperature is 3900 K and dT/dr is 0.9 K m(-1), resulting in a conductive power of 4.4 +/- 1 TW (1 TW = 10(12) Watt) flowing out of the core along the adiabatic gradient. New experimental results on the thermal conductivity of mantle minerals and new theoretical insights into the heat flow in mantle plumes support the case that the conductive power along the core's adiabatic gradient passing to the upper mantle can be transported away by both conduction and convection in the upper mantle. (C) 1998 Elsevier Science B.V. All rights reserved.