Topology optimization of microchannel heat sinks using a homogenization approach

• A topology optimization algorithm is formulated using a 3D-printing-compatible homogenization approach. • Multi-objective optimization is used to generate topologically optimized microchannel heat sink designs. • The topologically optimized designs are compared to optimized conventional heat designs. • The effects of hyperparameters used in the topology optimization process are studied. Topology optimization for heat sink devices typically relies on penalization methods to ensure the final designs are composed of strictly solid or open regions. In this work, we formulate a homogenization approach wherein the partial densities are physically represented as porous microstructures. This formulation allows design of thermal management components that have sub-grid features and leverages additive manufacturing techniques that can produce such partially porous regions within the build volume. Topology optimization of a liquid-cooled microchannel heat sink is presented for a hotspot over a uniform background heat input. The partial densities are represented as arrays of pin fins with varying gap sizes to achieve sub-grid-resolution features. To this end, the pin fins are modeled as a porous medium with volume-averaged effective properties. Height-averaged two-dimensional flow and non-equilibrium thermal models for porous media are developed for transport in the pin fin array. Through multi-objective optimization, the hydraulic and the thermal performance of the topologically optimized designs is investigated. The pin fin thickness is chosen based on the minimum reliable printing feature size of state-of-the-art direct metal laser sintering machines, and the gap sizes between the pin fins are optimized. The resulting topologies have porous-membrane-like designs where the liquid is transported through a fractal network of open, low-hydraulic-resistance manifold pathways and then forced across tightly spaced arrays of pin fins for effective heat transfer. The effects of the grid resolution and the initial design guess on the resulting topologies and performances are reported. The topologically optimized designs are revealed to offer significant performance improvements relative to the benchmark, a straight microchannel heat sink with features optimized under the same multi-objective cost function. The work demonstrates that representing partial densities as porous microstructures results in nearly resolution-independent performance at sufficiently-small grid sizes through the use of sub-grid features.