Topology optimization of microchannel heat sinks using a two-layer model

This paper investigates the topology optimization of microchannel heat sinks. A two-layer heat sink model is developed allowing to do topology optimizations at close to two-dimensional computational cost. In the model, reduced two-dimensional fluid dynamics equations proposed in the literature based on a plane flow assumption are adopted. By assuming a fourth-order polynomial temperature profile of the heat sink thermal-fluid layer and a linear temperature profile in the substrate, two-dimensional heat transfer governing equations of the two layers are obtained which are thermally coupled through an out-of-plane heat flux term. Topology optimizations of a square heat sink are carried out using the two-layer model. Comparison with a three-dimensional conjugate heat transfer analysis of optimized designs in COMSOL Multiphysics validates the accuracy of the two-layer model. The re-evaluation of an optimized design by a one-layer model commonly seen in the literature shows the inadequacy of the one-layer model in predicting physical fields properly. In addition, the influence of physical and optimization parameters on the layout complexity of optimized designs is studied and related to the Peclet number. Optimizations under diffusion-dominated conditions are performed and typical optimized topologies for heat conduction structures are seen.