A comparative study on the topology optimization design and performance of embedded liquid-cooled microchannels with different objective functions

In this study, a pseudo-three-dimensional topology method is employed to optimize the structure of embedded liquid-cooled microchannel heat sinks. Four typical heat transfer objective functions are considered: maximizing the enthalpy difference between inlet and outlet, minimizing the average temperature within the domain, maximizing the dimensionless heat transfer rate, and minimizing the equivalent thermal resistance. By selecting 27 combinations of penalty factors and Darcy numbers, the response curve characteristics of each objective function are systematically analyzed. Targeted improvements to the mathematical expressions of the objective functions are made to address non-monotonic response issues. The results show that different objective functions lead to distinct optimized topological structures. Improper selection of objective functions tends to generate physically meaningless intermediate density regions or even invalid solutions, such as “fully solid” or “fully void” configurations. Using the enthalpy difference as the objective yields' structures with low friction factors but poor heat dissipation performance. In contrast, structures obtained with the average temperature as the objective exhibit the best average heat dissipation performance. Compared with straight channel, the topology-optimized embedded microchannel heat sink raises PEC by up to 17.1% at equal Re and 49.8% at equal pressure drop.