Obtaining closure for a plane fin heat sink with elliptic scale-roughened surfaces for Volume Averaging Theory (VAT) based modeling

• A Volume Averaging Theory based model is developed for a plane fin heat sink with elliptic scale-roughened surfaces.
• The resulting rigorously derived closure terms are evaluated using a commercial CFD code.
• The results of closure term evaluation are presented in terms of correlations for friction factor and Nusselt number.
• The VAT based model is a function only of the porous media morphology and the closure.

Closure for a Volume Averaging Theory (VAT) based model of a plane fin heat sink (PFHS) with elliptic scale-roughened surfaces is obtained by evaluating the closure terms for the model using Computer Fluid Dynamics (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 efficiently solved for a wide range of parameters. 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 to obtain detailed solutions of flow and heat transfer through an element of the elliptic 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 CFD can be used in place of a detailed, often formidable, experimental effort to obtain closure for a VAT based model.