Adjoint Approach to Sensitivity Analysis of Convection Heat Transfer and Its Application to Heat Transfer Optimal Design

随着计算机硬件和数值模拟技术的发展，在给定边界条件的情况下，换热特性的数值预测成为可能。然而，从设计或控制的角度来看，在特定的边界条件下，对边界条件的预测比对特定边界条件下的换热特性的预测更为重要。在这项研究中，我们提出了一种伴随方法来反分析边界条件对对流换热问题的影响。该方法的主要特点如下：1.对于线性强迫对流问题，其伴随问题的数值解直接给出了在任意时刻控制换热的最优时间和空间热边界条件。对于一般的非线性对流问题，我们可以利用摄动原理推导出伴随系统。伴随解给了我们灵敏度，使我们能够在结合基于梯度的优化策略时同时优化热和流动边界条件。

With recent progress in computer hardware and numerical simulation techniques, numerical prediction of heat transfer characteristics has been possible when the boundary conditions are specified. However, from the viewpoint of design or control, the prediction of boundary conditions to achieve the desired heat transfer characteristics is more significant than that of heat transfer characteristics under specific boundary conditions. In other words, the problem becomes inverse one.In this study, we proposed an adjoint approach to inverse analysis of boundary condition effects on convection heat transfer problems. The main features of the present approach can be summarized as follows:1. For linear forced convection problem, a numerical solution of the adjoint problem directly gives us the optimal thermal boundary conditions both in time and space to control the heat transfer at any given time.2. For general nonlinear convection problems, we can derive an adjoint system using perturbation principle. The adjoint solution gives us the sensitivity which enables us to optimize both thermal and flow boundary conditions when combined with gradient-based optimization strategies.