Thermal History of the Earth with consideration of the Variable Thermal Conductivity of its Mantle

Abstract

Summary Data about the abundance of the radioactive elements and the thermal conductivity of the Earth are in favour of the view that its initial temperature To(r) must have been below the melting temperature. The results of the calculations of To(r) are presented for the Earth considered as being formed through accumulation of particles of a gas-dust protoplanetary cloud. The redistribution of radioactive elements is considered from uniform distribution to a layered one. The matter of the mantle is considered as a dielectric possessing not only molecular conductivity but a radiative transfer of heat in the high temperature range. The Green's function method and hydraulic analogy method are used for the calculations of the solution of the thermal conductivity equation. It is shown that the increase of effective thermal conductivity due to a radiative transfer of energy at a great depth does not produce any essential losses of inner heat. The thermal conductivity of the Earth's upper layers is largely determined by its molecular component decreasing as the temperature rises and thereby forbidding considerable losses of inner heat. That leads to the conclusion that the Earth's thermal history may be regarded as secular heating of its interior with simultaneous slight cooling of its outer layers.