Parametric Investigation of Viscous Dissipation Effects on Optimized Air Cooling Microchanneled Heat Sinks

Abstract

The effects of viscous dissipation of working fluid on the optimum heat sink parameters are investigated for the case of air cooling with a micro-/narrow-channeled compact heat sink. For this purpose, an optimization method is introduced first on the basis of dimensionless groups while employing several assumptions. This method yields minimum pumping work or pressure drop with a set of optimized geometric/hydrodynamic parameters when outer dimension of a heat sink and imposed thermal load are specified. Especially for the case of laminar flow, the procedure presents an explicit existence of cooling limit by the viscous heat generation, giving an analytical expression of the maximum removable heat Q max . The relationships between thermal load and each parameter are calculated for both laminar and turbulent regimes under the conditions of compact heat sink dimension (20 mm 2 20 mm 2 2 mm) and circular cross-sectional shape of channels. The results show that the cooling capability under such conditions is largely limited by the salient manifestation of viscous dissipation, when compared with our previous investigation on water cooling presented in [1]. From the discussion, it was concluded that when a micro-/narrow-channeled heat sink is to be designed with air, the effect of viscous dissipation should be taken into account in order to avoid falling on wrong optimum solutions.