Propagator matrix formulation of heat transfer in spherically stratified media

Abstract

In the paper we have transformed the steady and unsteady conductive heat transfer differential equation in spherical coordinates into a system of first order differential equations and processed them by method of propagator matrices to extrapolate the known surface heat flux and temperature to any desired depth. The elements of propagator matrices have been summarised for various piecewise continuous conductivity and rate of heat generation functions to approximate inhomogeneities in the earth. In the analysis the rate of heat generation is either assumed to depend linearly upon temperature or correspond to first order irreversible chemical reactions.