The development of cooling devices is important for many industrial products, and the lattice structure fabricated by additive manufacturing is expected to be useful for effective liquid cooling. However, lattice density should be carefully designed for an effective arrangement of coolant flow. In this research, we optimize the lattice density distribution using a lattice structure approximation and the gradient method. Fluid flow is approximated by deriving effective properties from the Darcy–Forchheimer law and analyzing the flow according to the Brinkman–Forchheimer equation. Thermal conduction and convection are also approximated as a weakly coupled problem. We use a simple basic lattice shape composed of pillars, optimizing only its density distribution by setting the pillar diameter as the design variable. Steady-state pressure and temperature reductions are treated as multi-objective functions. Through 2D and 3D numerical studies, we discuss the validity and limitations of the proposed method. Although observable errors in accuracy exist between the results obtained from the optimization and full scale models, relative performance optimization was considered successful.
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