矩形肋片热沉(火积)耗散率最小与最大热阻最小构形优化的比较研究

针对矩形肋片热沉, 分别以最大热阻最小化和基于(火积)耗散定义的当量热阻最小化为优化目标, 采用二维传热模型并结合有限元数值仿真对其进行构形优化, 比较了两种目标下的热沉最优构形, 并分析了全局参数(综合了对流换热系数、肋片占据的总面积及其热导率的函数)和材料占比对两种目标(最大热阻、当量热阻)及其对应最优构形的影响. 结果表明: 热沉外形固定时, 两种目标下均不存在最优的肋片厚度; 热沉外形自由变化时, 两种目标下的最优构形存在一定的差异. 此外, 全局参数对两种目标下的最优构形均没有影响, 而材料占比对两种目标下的最优构形均有较大影响. 提高全局参数和材料占比均可以减小最大热阻最小值和当量热阻最小值, 但对两种目标的减小程度不同. 总体上, 调节热沉结构参数使当量热阻最小, 可以同时获得很好的局部极限性能; 而调节热沉结构参数使最大热阻最小, 获得的整体平均散热性能却较差. 因此, 对本文热沉模型进行优化时, 以当量热阻最小化为优化目标更合理.

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 (φ), 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 φ= 0.4, respectively, compared with those for φ= 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.