Influence of bypass on flow through plate fin heat sinks

Forced air convection cooling of plate fin heat sinks is typically used as an effective means of cooling microelectronic devices because of its inherent simplicity and cost effectiveness. While the increased surface area obtained by placing plate fin heat sinks in close proximity to one another can significantly reduce the boundary resistance because of the added surface area, the added pressure drop associated with a constrained flow can lead to a decrease in inter-fin flow velocity along with a decrease in heat transfer. The ability to accurately predict the distribution of fluid flow between the fins of a heat sink and the fluid flow bypassing the heat sink is critical in the design and effective operation of heat sinks used to cool electronic components. An analytical model for predicting air flow and pressure drop across the heat sink is developed by applying conservation of mass and momentum over the bypass regions and in the flow channels established between the fins of the heat sink. The model is applicable for the entire laminar flow range and any type of bypass (side, top or both) or fully shrouded configurations. During the development of the model, the flow is assumed to be steady, laminar, developing flow. The model is found in good agreement with the experimental data over a wide range of flow conditions, heat sink geometries and bypass configurations, typical of many applications found in microelectronics and related fields. Data published in the open literature are also used to show the flexibility of the models to simulate a variety of applications. The model is also correlated to a simple equation within 12% confidence level for easy calculation of channel velocity through the heat sink when heat sink geometry, duct geometry and flow conditions are known.