Calculation of effective thermal conductivity of silicone matrix embedded with particulate phosphors in white led packages by 2D/3D unit cell method

The effective thermal conductivity (ETC) of silicone matrix embedded with particulate phosphors is of great importance in the thermal management of white light-emitting diode (LED) packages, not only because the mixture provides the heat dissipation path but also because the phosphors may generate heat as well. In this paper, a 2D/3D unit cell method with considering interface resistance was proposed to calculate the ETC of the silicone matrix embedded with particulate phosphors. To make the method more general, cubic, spherical and cylindrical particulate phosphors were calculated and discussed respectively. In order to validate the method, hot wire method was used to measure the thermal conductivity of phosphor silicone matrix. It is found that when the volume concentration increases from 0.038 to 0.25, the relative error between the experiments and calculations is within 5%. The ETC calculated by 2D model is slightly smaller than that by 3D model. The 3D model has relatively smaller critical concentration because the probability of forming continuous conductive chain by phosphor particles is lager in the 3D model than the 2D model. The shape of particle affect the ETC and the effect becomes more obvious at large concentration. The heat generated by phosphor particles is found to have no effect on the ETC.