论文标题
重新审视冷却鳍的最佳形状：使用最佳标准的一维分析研究
Revisiting the optimal shape of cooling fins: A one-dimensional analytical study using optimality criteria
论文作者
论文摘要
本文使用具有对流边界条件的一维热传导方程来重新讨论单个冷却鳍的最佳形状问题。首先，与以前的作品相比，我们根据需要使用优化问题的拉格朗日功能平稳的最佳条件采用一种方法。对于通常吹捧的恒定温度梯度条件，这产生了最佳条件基础。其次，我们试图最大程度地减少规定的热功率的根温度，而不是像以前的工作一样最大化恒定根温度的传热速率。最佳解决方案显示出对两者的完全等效，这似乎很明显，但据我们所知，以前尚未直接显示。最后，结果表明，最佳冷却鳍的生物数为1，在导电和对流电阻之间表现出完美的平衡。
This paper revisits the optimal shape problem of a single cooling fin using a one-dimensional heat conduction equation with convection boundary conditions. Firstly, in contrast to previous works, we apply an approach using optimality conditions based on requiring stationarity of the Lagrangian functional of the optimisation problem. This yields an optimality condition basis for the commonly touted constant temperature gradient condition. Secondly, we seek to minimise the root temperature for a prescribed thermal power, rather than maximising the heat transfer rate for a constant root temperature as previous works. The optimal solution is shown to be fully equivalent for the two, which may seem obvious but to our knowledge has not been shown directly before. Lastly, it is shown that optimal cooling fins have a Biot number of 1, exhibiting perfect balance between conductive and convective resistances.
