A Model for Flow Bypass and Tip Leakage in Pin Fin Heat Sinks

Abstract

A model for the pressure drop and heat transfer behavior of heat sinks with top bypass is presented. In addition to the characteristics of a traditional two-branch bypass model, the physics of tip leakage are taken into consideration. The total flow bypass is analyzed in terms of flow that is completely diverted and flow that enters the heat sink but leaks out. Difference formulations of the momentum and the energy equations were utilized to model the problem in the flow direction. Traditional hydraulic resistance and heat transfer correlations for infinitely long tube bundles were used to close the equations. Tip leakage mechanisms were modeled by introducing momentum equations in the flow normal direction in both the pin side and bypass channel, with ad hoc assumptions about the static pressure distribution in that direction. Although the model is applicable to any kind of heat sink, as a case study, results are presented for in-line square pin fin heat sinks. Results were compared with the predictions from a two-branch bypass model and previous experimental data. It is shown that tip leakage effects are important in setting the overall pressure drop at moderate and high pin spacing, but have only minor influence on heat transfer.