Geothermic models of variable thermal conductivities and source functions

Abstract

Temperature distributions are investigated for the stratified earth having planar and spherical boundaries under the assumptions of (i) Steady state heat flow (ii) layered non-uniform distribution of sources, and (iii) non-uniform thermal conductivities in each individual layer. The non-uniformity in source conditions and conductivity distributions is approximated by exponential and generalized power law functions of depths. The corresponding heat conduction equations are solved so as to satisfy an appropriate set of boundary conditions. The solutions will be useful in providing an analytical basis for an accurate and reliable description of the (a) thermal structure for a variety of new models, and (b) complex interplay of source and conductivity variations in defining possible temperatures in the interior of the earth.