Graded foam-filled channels are a very promising solution for improving the thermal performance of heat sinks because of their customized structures that leave large amounts of room for heat transfer enhancement. Accordingly, this paper proposes a comprehensive optimization framework to address the design of such components, which are subjected to a uniform heat flux boundary condition. The graded foam is achieved by parameterizing the spatial distributions of porosity and/or Pores Per Inch (PPI). Mono- and multi-objective optimizations are implemented to find the best combination of the foam’s fluid-dynamic, geometrical and morphological design variables. The mono-objective approach addresses the Performance Evaluation Criterion (PEC) as an objective function to maximize the thermal efficiency of graded foams. The multi-objective approach addresses different objective functions by means of Pareto optimization to identify the optimal tradeoff solutions between heat transfer enhancement and pressure drop reduction. Optimizations are performed by assuming a local thermal non-equilibrium in the foam. They allowed us to achieve a 1.51 PEC value with H* = 0.50, Re_H = 15000, i_ε = i_PPI = 0.50, ε(0) = 0.85, ε(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and k_s→f = 10⁴ as the design variables. For the three multi-objective functions investigated, one can extrapolate the optimum from the Pareto front via the utopia criterion, obtaining $\overline{h}$ = 502 W/m² K and Δp = 80 Pa, $\overline{{\mathrm{Nu}}_{\mathrm{H},\mathrm{unif}}}$ = 2790 and f = 42, $\overline{{⟨T_s^{*}⟩}^s}$= 0.011, and Δp* = 91. The optimal solutions provide original insights and guidelines for the thermal design of graded foam-filled channels.

Additive manufacturing is now a promising option to obtain porous customized structures at relatively low scales. The capability to design structures with tunable heat transfer performance compared to conventional porous materials, such as open-cell foams, is very interesting to the user. In this study, we investigated heat conduction in a drilled-hollow-sphere architected foam, inspired by Triply-Periodic Minimal Surfaces (TPMS) and foam structures, generated using perforated spherical hollow shells connected with cylindrical binders. Temperature fields and heat fluxes in the foam were predicted numerically, and the effective thermal conductivity of the foam was calculated for different sets of the binder angle, the shell thickness, and the perforation radius. The dependence of the foam porosity on the binder angle and perforation radius was also pointed out. Predictions were validated by comparing them with data available from the literature. Results showed that varying the characteristics of the investigated drilled-hollow-sphere architected foam, its predicted effective thermal conductivity can be adjusted by more than one order of magnitude larger or smaller than that of conventional foams, making architected foams promising enhancers of their heat transfer performance. Finally, new dimensionless correlations among the effective thermal conductivity and some significant morphological parameters of the foam were derived and presented for practical use.