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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, ReH = 15000, iε = iPPI = 0.50, ε(0) = 0.85, ε(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and ks→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 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.

Most European buildings built before 1980s were constructed without any design concern for energy efficiency and environmental sustainability. In addition to this issue, over the last decades, the essential need of safer buildings has progressively attracted the interest of scientific community and government institutions. However, the strong interaction between energy and structural aspects in building retrofit design has never been handled via robust and reliable approaches. The present study explores this knowledge gap by introducing a novel multi-step approach that addresses the retrofit of existing buildings by integrating energy, structural and economic aspects. To this end, a multi-stage energy optimization is carried out by implementing a genetic algorithm and a smart research strategy. Thus, the cost-optimal energy retrofit solution is identified and the impact of the expected economic losses due to seismic damage is assessed throughout the building lifecycle. The methodology is applied to a multi-story residential building, considering the effects of two different building locations, namely Milan and Norcia. These latter are characterized by similar climatic conditions but by a different level of seismic risk, which is higher for Norcia. The outcomes show that the estimated seismic economic losses associated with the energy retrofit solutions are strongly affected by the building location. Thus, the selection of the optimal energy retrofit measures should be related to the building structural behavior in order to achieve reliable economic and sustainability benefits.