Volume Averaging Theory (VAT) based modeling and closure evaluation of scale-roughened plane fin heat sink

The present paper describes an effort to model a plane fin heat sink (PFHS) with scale-roughened surfaces based on Volume Averaging Theory (VAT) and evaluate the closure terms of the model using CFD code. Modeling a PFHS as porous media based on VAT, specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts and the VAT based governing equations can be solved for a wide range of heat sink designs. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a Representative Elementary Volume (REV). The terms in the closure expressions are complex and sometimes relating experimental data to the closure terms is difficult. In this work we use CFD code to obtain detailed solutions of flow and heat transfer through an element of the scale-roughened heat sink and use these results to evaluate the closure terms needed for a fast running VAT based code, which can then be used to solve the heat transfer characteristics of a higher level heat sink. The objective is to show how heat sinks can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort to close the VAT based model.