Mono- and Multi-Objective CFD Optimization of Graded Foam-Filled Channels

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 = i_PPI = 0.50, ε(0) = 0.85, ε(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and k = 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 h¯ = 502 W/m² K and Δp = 80 Pa, NuH,unif¯ = 2790 and f = 42, ⟨Ts*⟩s¯= 0.011, and Δp* = 91. The optimal solutions provide original insights and guidelines for the thermal design of graded foam-filled channels.