论文标题
微通道冷却系统的形状灵敏度分析
Shape Sensitivity Analysis for a Microchannel Cooling System
论文作者
论文摘要
我们分析了微通道冷却系统的形状优化问题的理论框架。为此，引入了基于冷却器吸收能量以及冷却系统子域中的一些所需流量的成本功能。冷却液的流量和温度是由耦合到对流扩散方程的Stokes系统建模的。我们证明了该模型在通过速度方法转换的域上的良好性。此外，我们严格地证明我们优化问题的成本功能是可差异的，并通过最近的材料衍生衍生物的无伴随方法来计算其形状衍生物。
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.
