fig5

Figure 5. Representative TO workflows relevant to liquid-cooling and multiphysics design. (A) MMC-SIMP hybrid topology optimization process, including design-variable definition, element-density construction, objective and constraint formulation, finite-element analysis, sensitivity analysis, design-variable update, and convergence checking; (A) is reprinted with permission from Ref.^[112]. Copyright © 2025 Springer Nature; (B) Framework for length-scale-controlled topology-optimized cold-plate design and fabrication, with validation of thermal and flow performance; (B) is reprinted with permission from Ref.^[99], under the terms of the CC BY 4.0 license. (C) Immersed level-set thermo-mechanical TO workflow, integrating thermal and mechanical analyses, objective-function evaluation, sensitivity calculation, level-set evolution, constraint treatment, and convergence checking; (C) is reprinted with permission from Ref.^[113], under the terms of the CC BY 4.0 license. TO: Topology optimization; MMC: moving morphable component; SIMP: solid isotropic material with penalization; MMA: method of moving asymptotes.