微通道冷却系统的形状灵敏度分析
Shape Sensitivity Analysis for a Microchannel Cooling System
AI总结：
本文研究微通道冷却系统的形状优化问题，通过Stokes系统与对流扩散方程建模，严格证明了成本泛函的适定性与形状可微性，并利用无物质导数伴随方法计算了形状导数。
摘要：
我们分析了微通道冷却系统形状优化问题的理论框架。为此，引入了一个基于跟踪冷却器吸收的能量以及冷却系统子区域上某期望流动的成本泛函。冷却剂的流动和温度由耦合对流扩散方程的Stokes系统建模。我们证明了该模型在通过速度方法变换的域上的适定性。此外，我们严格证明了优化问题的成本泛函是形状可微的，并利用一种最近的无物质导体伴随方法计算了其形状导数。
英文摘要：
We analyze the theoretical framework of a shape optimization problem for a microchannel cooling system. To this end, a cost functional based on the tracking of absorbed energy by the cooler as well as some desired flow on a subdomain of the cooling system is introduced. The flow and temperature of the coolant are modeled by a Stokes system coupled to a convection diffusion equation. We prove the well-posedness of this model on a domain transformed by the speed method. Further, we rigorously prove that the cost functional of our optimization problem is shape differentiable and calculate its shape derivative by means of a recent material derivative free adjoint approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
