Mathematical model and computation of heat distribution for LED heat sink

The light-emitting diode (LED) has many advantages over conventional lighting including lower energy consumption, longer lifetime, improved physical robustness, smaller size, and faster switching. It is noted, however, that its efficiency and lifetime will be degraded severely when it is operated at high temperature. Both previous simulations and experimental results have already indicated that the heat transfer in vertical direction of the LED lamp by conduction is the critical component. In this paper, a simplified mathematical model of the heat source and the conduction distribution for the LED heat sink is developed to estimate the heat distribution in the spherical coordinate system, which can be used for the shape optimization design. Furthermore, the model of the heat conduction equation is solved numerically with the explicit finite-difference method (EFDM). Several numerical simulations show that the model performs well when considering the real situation, so our method is feasible and effective.