Comparative study on constructal optimizations of rectangular fins heat sink based on entransy dissipation rate minimization and maximum thermal resistance minimization

Constructal optimization of a rectangular fin heat sink with two-dimensional heat transfer model is carried out through using numerical simulation by finite element method, in which the minimized maximum thermal resistance and the minimized equivalent thermal resistance based on entransy dissipation are taken as the optimization objectives, respectively. The optimal constructs based on the two objectives are compared. The influences of a global parameter (a) which integrates convective heat transfer coefficient, overall area occupied by fin and its thermal conductivity, and the volume fraction (phi), on the minimized maximum thermal resistance, the minimized equivalent thermal resistances and their corresponding optimal constructs are analyzed. The results show that there does not exist optimal thickness of fins for the two objectives when the shape of the heat sink is fixed, and the optimal constructs based on the two objectives are different when the shape of the heat sinks can be changed freely. Besides, the global parameter has no influence on the optimal constructs based on the two objectives, but the volume fraction does. The increases of the global parameter and the volume fraction reduce the minimum values of the maximum thermal resistance and the equivalent thermal resistance, but the degrees are different. The reduce degree of the global parameter to the minimized equivalent thermal resistance is larger than that to the minimized maximum thermal resistance. The minimized equivalent thermal resistance and the minimized maximum thermal resistance are reduced by 40.03% and 41.42% for a = 0.5, respectively, compared with those for a = 0.3. However, the reduce degree of the volume fraction to the minimized maximum thermal resistance is larger than that to the minimized equivalent thermal resistance. The minimized equivalent thermal resistance and the minimized maximum thermal resistance are reduced by 59.69% and 32.80% for phi = 0.4, respectively, compared with those for phi = 0.3. As a whole, adjusting the parameters of the heat sink to make the equivalent thermal resistance minimum can make the local limit performance good enough at the same time; however, the overall average heat dissipation performance of the heat sink becomes worse when the parameters of the heat sink are adjusted to make the maximum thermal resistance minimum. Thus, it is more reasonable to take the equivalent thermal resistance minimization as the optimization objective when the heat sink is optimized.