Analysis and Design of a Least Material Orthotropic Pin Fin Heat Sinks

The thermal anisotropy inherent in pin fins fabricated of polymer matrix composites necessitates the use of two-dimensional orthotropic relations for the prediction of the temperature distribution and heat transfer rate in large Biot number fins. Such fins offer a promising alternative to conventional metallic fins and heat sinks for electronic cooling applications, providing the benefits of moldability, lower density, lower fabrication energy and reduced cost. To realize these benefits and to compete favorably with the heat rejection capability of metallic fins and heat sinks, the polymer composite components must be thermally-optimized for the least-material configuration. This paper begins with a brief review of the available literature and a previously derived rigorous analytic model for orthotropic pin fins. The parametric trends are explored and attention is focused on identifying the least-material pin fin aspect ratio for a range of volumes and operating conditions. The orthotropic least-material configuration is found to closely approximate the aspect ratio associated with an isotropic fin. Simplified equations are proposed and analyzed for the cooling rate of an orthotropic pin fin. Further it is combined together with the least-material relation in order to design a least-material natural convection heat sink. The performance of the polymer least-material heat sinks is evaluated and compared, using common metrics, to conventional aluminum heat sinks