Heat Conduction Within an Elastic Earth

We use theoretical results derived in a previous paper (Lanzano, 1986) to numerically evaluate the temperature profile and radial deformation within a spherical, elastic Earth due to heat generated by the decay of radiogenic elements. We consider only the Uranium family and have assumed the diffusivity of the silicate mantle to be K = 8 × 10^-3 cm² s^-1, the Poisson elastic ratio to be Σ = 0.25 and the coefficient of thermal expansion to be α = 2 × 10^-5 (deg)^-1. Our series solutions when applied to the interiors of the Moon, Mercury, and Mars yield results in agreement with Kopal's (1963) evaluations.