Parameter-free Shape Optimization of Heat Sinks

In this paper, we present a parameter-free shape optimization approach for designing heat sinks. In our optimization formulation, we use a weighted combination of thermal (outlet temperature) and hydraulic (pressure drop) performances as the objective function with the fin volume as a constraint. The governing Navier–Stokes fluid flow and advective heat transfer equations are solved by a finite element method. In this shape optimization approach, all finite element nodes of design boundaries serve as optimization variables, without extraneous parameterization of boundary shape. We derive analytical form of shape gradient and use it to drive the boundary evolution during the optimization. Numerical examples of simultaneous optimization of multiple fins are given. The optimized heat sinks exhibit superior thermohydraulic performances than those from traditional sizing optimization.