Modeling Forced Convection in Finned Metal Foam Heat Sinks

A numerical study has been undertaken to explore the details of forced convection heat transfer in finned aluminum foam heat sinks. Calculations are made using a finite-volume computational fluid dynamics (CFD) code that solves for the flow and heat transfer in conjugate fluid/porous/solid domains. The results indicate that using unfinned blocks of porous aluminum results in low convective heat transfer due to the relatively low effective thermal conductivity of the porous aluminum. The addition of aluminum fins to the heat sink significantly enhances the heat transfer with only a moderate pressure drop penalty. The convective enhancement is maximized when thermal boundary layers between adjacent fins merge together and become nearly developed for much of the length of the heat sink. It is found that the heat transfer enhancement is due to increased heat entrainment into the aluminum foam by conduction. A model for the equivalent conductivity of the finned/foam heat sinks is developed using extended surface theory. This model is used to explain the heat transfer enhancement as an increase in equivalent conductivity of the device. The model is also shown to predict the heat transfer for various heat sink geometries based on a single CFD calculation to find the equivalent conductivity of the device. This model will find utility in characterizing heat sinks and in allowing for quick assessments of the effect of varying heat sink properties.