Effective thermal conductivity of graded nanocomposites with interfacial thermal resistance

This work employs the self-consistent method to investigate the effective thermal conductivity distribution in functionally graded materials (FGMs) considering the Kapitza interfacial thermal resistance. A heat conduction solution is first derived for one spherical particle embedded in a graded matrix with a prefect interface. The interfacial thermal resistance of a nanoparticle is simulated by a new particle with a lower thermal conductivity. A novel self-consistent formulation is developed to derive the averaged heat flux field of the particle phase. Then the temperature gradient can be obtained in the gradation direction. From the relation between the effective flux and temperature gradient in the gradation direction, the effective thermal conductivity distribution is solved. If the gradient of the volume fraction distribution is zero, the FGM is reduced to a composite containing uniformly dispersed nanoparticles and a explicit solution of the effective thermal conductivity is provided. Disregarding the interfacial thermal resistance, the proposed model recovers the conventional self-consistent model. Mathematically, effective thermal conductivity is a quantity exactly analogous to effective electric conductivity, dielectric permittivity, magnetic permeability and water permeability in a linear static state, so this method can be extended to those problems for graded materials.