Numerical evaluation of pressure and temperature effects on thermal conductivity: Implications for crustal geothenns

Abstract

Pressure and temperature effects on the thermal conductivity of crustal rocks are discussed on the basis of published data. The solution of the steady-state conductive heat equation with pressure-dependent thermal conductivity and heat production leads to a complex non-linear form. Two solutions are discussed: (i) an analytical solution based on an approximation of the transcendental integrals; (ii) a numerical solution using a finite-difference scheme. In both cases, the heat production due to radiogenic elements is assumed to decay exponentially with depth. An example based on a 3-layer continental structure was solved in order to evaluate the temperature differences at a depth of 35 km (Moho discontinuity). A surface heat flow ranging between 50 and 110 mW/m2 was assumed. The calculations show that the pressure effect on termal conductivity can be neglected in the uppermost layers, but for large surface heat flow values, the effect can be important below 5 km.