Mathematical Model And Numerical Simulations Of The Heat Distribution For LED Heat Sink

LED, that is short for Light emitting diode, is a kind of solid state semi-conductor device which directly converts electrical energy into light. In actual application, in order to produce more light output, the higher power must be applied to LED. However, it has been found that the efficiency and lifetime will be degraded greatly when it is operated at a high temperature. For some high-power LEDs, heat sinks are required to keep the temperature in a reasonable range when they are operated, thus it is very important to consider the designs of heat sinks used to cool LED.The cooling methods of LED mainly include three parts:flow, radiation and conduction. Though a wide range of heat sinks in different shapes, sizes, and structures are currently used in the commercial LED light bulbs, while most of these heat sinks were not optimized in terms of cooling efficiency, dimension, and material cost. So the optimization research of heat dissipation for LED is a very practical application work. It is very necessary to get the heat distribution of LED when we try to optimize the design of LED heat sink. The objective of our present work is building a simplified mathematical model for the heat distribution of LED heat sink, which is useful for its shape optimization design. The LED considered in this work is a simple daily used LED lamp, which is vertically placed, and the external environmental temperature is constant.Now, both previous simulation and experimental results have already indi-cated that the heat transfer in vertical direction of the LED lamp by conduction is the most critical component. Thus, we mainly consider the conduction part of LED heat sink in this work, and a heat conduction equation is described. A sim-plified heat conduction equation model(regardless its top cover and base) which considers the top and the base of LED lamp as spherical, is built step by step to estimate the heat distribution for LED heat sink. It can be rapidly computed the static heat distribution and the temperature in different designs of similar LED heat sinks. The built simplified heat conduction model is in the spherical coordinate system. We give some boundary conditions to solve the built heat conduction equation, which can be proved the validity by the following numeri-cal simulations of heat distribution. To the built boundary conditions and heat condition equation, the explicit and implicit finite difference method would be provided respectively, and the stablity of the built methods would also be stud-ied. The following numerical simulations of heat distribution could demonstrate our built mathematical models are well conform to the reality. The improved implicit finite difference method is much better. Our work would be useful for the shape optimization design of LED heat sinks. It provides a better a trade-off between material cost and temperature distribution.