Optimum Design of Heat Sink by Using Differential Evolution and Simplex Method

The optimum design of the heat sink by using differential evolution (DE) method is discussed in the present paper. The DE strategy (DE/ best/ 1/exp) is used here because this strategy is best strategy for heat transfer applications [1]. The main procedures for the heat sink optimization is found the minimum thermal resistance (maximize the heat transfer per unit volume) of the heat sink in order to reduce the cost of heat sink by reducing the heat sink material. The main design parameters (the fin diameter, df, the fin length, Lf, number of fins, Nf, the approach velocity, Uapp, stream wise pitch, SL, span wise pitch, ST) assumed varied between lower and upper values during the present study to get the minimum thermal resistance. The overall dimension of the heat sink and the pressure drop across the heat sink are taken as deign constrains. After applying the DE for the case study in the present paper, the optimum thermal resistance for maximize the heat transfer from inline fin arrangement heat sink is found (0.500467 Cْ/W) and for staggered fin arrangement heat sink is found (0.4021 Cْ/W). The effect of the constant parameters (the thickness, dimensions and material of the base plate) on the minimum thermal resistance is discussed. Also, the effect and selections of the differential evolution parameters (crossover coefficient (CR) and scaling factor (F)) on the generation (iteration time) are examined. The optimum values of F & CR that minimize the generation for attaining the minimum thermal resistance are (F=0.9 & CR=0.8) . Also, the results of the DE are compared with Nelder Mead simplex method for same case study in order to check the accuracy and efficiency of the DE method. The DE was consumed less time than the simplex method for the same present case study.