Heat transfer through a three-phase porous medium

Abstract

Experimental values of the effective thermal conductivity obtained by Sugawara on calcareous sandstone partially filled with water are compared with values calculated by using the geometric mean equation of Lichteneker extended to a system having three phases and also with values obtained from a relation given by Brailsford and Major. The calculated values disagree with the experimental values. A weighted geometric mean of the maximum (weighted arithmetic mean of the individual thermal conductivities) and minimum (weighted harmonic mean of the individual thermal conductivities) values of the thermal conductivity of the sample is proposed here for obtaining its effective thermal conductivity. It is held that such an equation can demonstrate the structure and distribution of phases in the sample.