Abstract
Light-emitting diode (LED) has higher efficiency and longer lifetime when compared with the conventional lighting. However, the efficiency and lifetime will be degraded greatly when it is operated at a high temperature. Now, both previous simulation and experimental results have already indicated that the heat transfer in vertical direction of the LED lamp by conduction is the most critical component. In this paper, a simplified numerical simulation model is built to estimate the heat distribution of the LED heat sink in the spherical coordinate system, which would be useful for its shape optimization design. With this model, some mathematical treatments are provided to a heat conduction equation, in order to rapidly compute the static heat distribution and the temperature of different designs of LED heat sinks. The built rapid heat sink evaluation method, implicit finite difference method (IFDM), is unconditionally stable. Several heat distribution simulations could demonstrate that our built mathematical model conforms well to the reality and our method is full of feasibility and effectiveness.
Highlights
Light-emitting diode (LED) lamp has played an important role in the illumination market, mainly due to the advantages of more compact package in size, higher efficiency, and longer lifetime than the conventional lighting types
The design of heat sink used to cool light-emitting diode (LED) lamp is full of importance to ensure their long lifetime and high efficiency
To the technique of computer, the large size of iterative matrix M which is a multiplication of mesh nodes about N2, M2, M3, N3, and N4 is a great challenge when we want much denser mesh dissections
Summary
Light-emitting diode (LED) lamp has played an important role in the illumination market, mainly due to the advantages of more compact package in size, higher efficiency, and longer lifetime than the conventional lighting types. The objective of our present work is building a simplified mathematical model and developing a rapid heat sink evaluation method by making some mathematical treatments, that is, the implicit finite difference method (IFDM), to a heat conduction equation in the spherical coordinate system for the LED heat sink. With this method, we can estimate the static heat distribution and the temperature in different designs of LED heat sink.
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