Effective Thermal Conductivity of Continuous Matrix-spherical Dispersed Phase Composite with Single-point Interfacial Thermal Contact: Continuum Regime Gas Conduction in the Gap

Abstract

Analytical solutions are presented for the effective thermal conductivity of a continuous matrix composite with fully debonded spherical inclusions in single-point contact with the matrix. This situation represents the lower bound on the effect of partial debonding between the dispersed and the matrix phase on composite thermal conductivity. The heat transfer across the gap in the debonded regions is assumed to occur by gaseous conduction. Solutions for the temperature gradient parallel and perpendicular to the point of contact are considered. Numerical results for a sodaborosilicate glass matrix with spherical nickel inclusions and a range of values for the thermal conductivity k _gap of the gas phase in the gap are presented. The effective composite thermal conductivity values for gradients imposed parallel and perpendicular to the point of contact were found to differ significantly depending on the magnitudes of the contact conductance and the thermal conductivity of the gas. When k _gap approaches zero, the solution approaches that for a matrix with spherical pores presented by Maxwell. When k _gap approaches infinity, the composite thermal conductivity approaches Maxwell’s value for a composite with perfect interfacial thermal contact.