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.

Recent advancements in additive manufacturing technologies are increasing the feasibility and ease of manufacturing of ever more intricate architected porous materials for use in heat transfer devices. One such architected porous material of interest to many researchers are triply periodic minimal surface (TPMS) structures, which have geometries that are defined by a set of trigonometric functions. In this study we investigated heat conduction in TPMS structures generated in MATLAB using COMSOL multiphysics numerical simulations. Effective thermal conductivity was predicted numerically in TPMS structures using a novel approach to correlate tortuosity to structure in Diamond, Fischer-Koch, Gyroid, IWP, and Primitive TPMS structures across a range of solid volume fractions. Results showed that both tortuosity and effective thermal conductivity are functions of both TPMS type and solid volume fraction. Empirically correlating tortuosities to the well-known Bruggeman equation has been presented, and the predicted effective thermal conductivities were compared to published experimental TPMS heat conduction data and analytical correlations for heat conduction in other porous materials. An inverse Boolean operation was performed on each TPMS structure so correlation between tortuosity and heat conduction in the so-called inverse TPMS domain was also evaluated. These results may be used in the fine tuning of TPMS-based heat transfer devices, and to better understand and characterize transport properties in TPMS structures.