Effective thermal conductivity (ETC) of composite materials is an important lumped parameter to describe heat conductions inside composite materials without dealing with complex structures. When particles release heat inside composite materials, like particle-filled nuclear fuel elements, classical ETC models are not appropriate and the effect of inner heat source requires further investigation. In our previous researches, heat conductions with inner heat sources were analyzed and the ETCs were redefined to predict the average temperatures of composite materials. Current work continued to study the ETC model of spherical composite materials with distributed heat-releasing particles. In the spherical two-phase composite material, a number of identical particles were dispersed in the matrix and the heat released from each particle was the same. Given the uniformly distributed positions of particles, the ETC model of spherical composite materials was proposed by the combination of 3 terms and validated by finite element simulations. The new ETC model was also discussed and compared with classical models by various particle numbers, particle sizes and particle-matrix thermal conductivities. Furthermore, cases of randomly distributed particles were also simulated to account for the deviations from the proposed ETC model. The new ETC model in this paper reveals the heat conduction mechanism in composite materials with distributed inner heat sources. It also showed the potential to be applied in thermal hydraulic analyses of nuclear reactors with particle-filled fuel elements.
Liu et al. (2025) studied this question.