Numerical study of three-dimensional microchannel using the Constructal Law

Abstract

In this work it was performed a numerical study about the design of the fins geometry of a microchannel heat sink. The study was based on the Constructal Theory and proposes to develop a methodology to predict, in a deterministic way, the positioning and size of the heat sink fins. The method uses a construction function, which is dependent on velocity and temperature fields, to “guide” the construction. Main goal is to obtain arrangements with the lowest possible thermal resistance. The OpenFOAM software was used to solve the model equations using the Finite Volume method. The geometries were built from an empty domain to which fins were added. A total of 12 geometries were generated and best results were obtained with the geometries that better combined a large fins occupation area with a low coolant flow rate. It was also showed that there is a correct amount of solid which leads to the best thermal performance. Observing the best obtained configurations, it is clear that there is a limit to the material addition in the channel; flow restriction causes a drop in the flow rate which is not compensated by the increase in the heat sink solid volume.