Minimisation of heat sink mass using mathematical optimisation

Heat sink designers have to balance a number of conflicting parameters to maximise the performance of a heat sink. This must be achieved within the given constraints of size or volume of the heat sink as well as the mass or material cost of the heat sink. This multi-parameter problem lends itself naturally to optimisation techniques. Traditionally, an experimental approach was used where different heat sink designs were constructed and their performance measured. This approach is both time-consuming and costly. More recently, numerical CFD techniques have been used, but mostly on a trial-and-error basis. This leads to long design cycles and is basically the numerical equivalent of the experimental approach. A better approach is to combine a semi-empirical simulation program with mathematical optimisation techniques. This paper describes the use of mathematical optimisation techniques to minimise heat sink mass or thermal resistance using five design variables. They are heat sink fin height, fin thickness, extrusion length base thickness and number of fins for the heat sink. The simulation uses the Qfin 2.1 code, while the optimisation is carried out by means of the DYNAMIC-e method. This method is specifically designed to handle constrained problems where the objective and/or constraint functions are expensive to evaluate. The paper illustrates how the parameters considered influence the heat sink mass and how mathematical optimisation techniques can be used by the heat sink designer to design compact heat sinks for different types of electronic enclosures