| Summary: | 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 <i>H*</i> = 0.50, Re<sub>H</sub> = 15000, <i>i<sub>ε</sub></i> = i<sub>PPI</sub> = 0.50, <i>ε</i>(0) = 0.85, <i>ε</i>(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and <i>k<sub>s</sub></i><i><sub>→f</sub></i> = 10<sup>4</sup> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>h</mi><mo stretchy="true">¯</mo></mover></mrow></semantics></math></inline-formula> = 502 W/m<sup>2</sup> K and Δ<i>p</i> = 80 Pa, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><msub><mrow><mi>Nu</mi></mrow><mrow><mrow><mi mathvariant="normal">H</mi><mo>,</mo><mi>unif</mi></mrow></mrow></msub></mrow><mo stretchy="true">¯</mo></mover></mrow></semantics></math></inline-formula> = 2790 and <i>f</i> = 42, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mrow><msup><mrow><mrow><mo>⟨</mo><mrow><msubsup><mi>T</mi><mi>s</mi><mo>*</mo></msubsup></mrow><mo>⟩</mo></mrow></mrow><mi>s</mi></msup></mrow><mo stretchy="true">¯</mo></mover></mrow></semantics></math></inline-formula>= 0.011, and Δ<i>p*</i> = 91. The optimal solutions provide original insights and guidelines for the thermal design of graded foam-filled channels.
|
|---|