Constructal design of combined microchannel and micro pin fins for electronic cooling

This paper presents a three-dimensional numerical study of steady, laminar, incompressible flow and forced convection heat transfer through a microchannel heat sink with micro pin fin inserts for both fixed and variable axial lengths. The objective of the study was to optimise the geometric configuration of an integrated microchannel and micro pin fins for different solid volumes so that the peak temperature in the configuration was minimised. The effect of the micro pin fins on the optimised microchannel was also investigated. The geometric optimisation of the integrated microchannel and micro pin fin was carried out using a computational fluid dynamics (CFD) code with a goal-driven optimisation tool subject to global constraints. The optimisation procedure was carried out in two steps. Firstly, the microchannel configuration was optimised without the micro pin fins inserted and the results were compared with similar work found in the open literature. This optimisation was carried out for both fixed and relaxed lengths. Thereafter, the integrated design of the microchannel and micro pin fins was optimised. The effect of the Bejan number on the solid volume fraction, channel aspect ratio and hydraulic diameter, pin fin aspect ratio, minimised peak temperature and maximised thermal conductance were reported. Results showed that as the Bejan number increased, the minimised peak temperature decreased. Also, the maximum thermal conductance increased with the optimised microchannel structure with three to six rows of micro pin fin inserts. Diminishing return set in when the number of rows of micro pin fin inserts was greater than three for the fixed length but for the relaxed length, as the number of rows increased, the results improved but when it exceeded six diminishing returns set in for a fixed solid volume of 0.9mm3. For each Bejan number used in this study, there was an optimum channel hydraulic diameter and aspect ratio, solid volume fraction and pin fin aspect ratio that satisfied the global objective.