Designing parameter optimization of a Parallel-Plain Fin heat sink using the grey-based fuzzy algorithm with the orthogonal arrays

In this paper, a grey-based fuzzy algorithm with the orthogonal arrays is employed to find the optimal designing parameters' setting for a heat sink with the Parallel-Plain Fin (PPF) on the multiple thermal performance characteristics. The proposed algorithm, coupling the grey relational analysis with the fuzzy logic, obtains a grey–fuzzy reasoning grade to evaluate the multiple performance characteristics according to the grey relational coefficient of each performance characteristic. In the present study, the designing parameters of the heat sink include the height of fin, the width of gap between fins, the width of slot, the number of slot and the air speed. The design of experiment (DOE) adopts the L₁₆(4⁵) orthogonal arrays table which is four levels and five factors type of factorial design. The average convective heat transfer coefficient, the thermal resistance and the pressure drop are considered as the multiple thermal performance characteristics and explored in the experiment. In addition, the response table, response graph and the analysis of variance (ANOVA) are used to find the optimal settings and the influence of designing parameters on the multiple performance characteristics. The results of confirmation tests with the optimal settings of designing parameters have obviously shown that the multiple thermal performance characteristics are effectively improved through these procedures.