There is growing interest in the use of polymer composites with enhanced thermal conductivity for high performance fin arrays and heat sinks. However, the thermal conductivity of these materials is relatively low compared to conventional fin metals, and strongly orthotropic. Therefore, the design and optimization of such polymer pin fins requires extension of the one dimensional classical fin analysis to include two-dimensional orthotropic heat conduction effects. An analytical equation for heat transfer from a cylindrical pin fin with orthotropic thermal conductivity is derived and validated using detailed finite-element results. The thermal performance of such fins was found to be dominated by the axial thermal conductivity, but to depart from the classical fin solution with increasing values of a radius- and radial conductivity-based Biot number. Using these relations, it is determined that fin orthotropy does not materially affect the behavior of typical air-cooled fins. Alternatively, for heat transfer coefficients achievable with water cooling and conductivity ratios below 0.1, the fin heat transfer rate can fall more than 25% below the “classical” heat transfer rates. Detailed orthotropic fin temperature distributions are used to explain this discrepancy. Simplified orthotropic pin fin heat transfer equations are derived and validated over a wide range of orthotropic conditions.
Numerical Simulation of Natural Convection Heat Transfer using Solid and Hollow/Perforated Pin Fin Heat Sinks