A design problem to estimate the optimal fin shape of LED lighting heat sinks

A fin shape design problem is considered in the present work utilizing the Levenberg-Marquardt Method (LMM) and a commercial package CFD-ACE+. The objective is to design the optimal fin shape of radial heat sink for light-emitting diode (LED) lighting devices and to enhance the cooling performance of the heat sink. The design process is to obtain the optimal design variables for the external fin shape of the heat sink and then minimize the average temperature of the bottom surface of heat sink. The natural convection working condition of the heat sink is assumed as the working condition, besides, the effect of radiation heat transfer between heat sink and air is also included. Numerical results indicate that by utilizing the fin heights as the design variables, the best heat sink performance can be obtained and the middle and center fin height both become negligible. The system thermal resistance of the optimal design can be reduced further by 16.8% and 11.0% than the initial and Type 2 design heat sinks, respectively. Finally, three types of heat sinks with fins are carried on the experimental verification. The results from experiments show that with the designed optimal fin shapes the cooling performance of the heat sink is indeed better than those with the initial and existing fin designs, besides, the numerical and experimental temperature distributions on the measured surfaces are very much similar. The physical argumentation of this work lies in that the approach presented in this work could result in a better design for fin shape of LED lighting heat sinks and can be applied in reality.