Manifold microchannel heat sink design using optimization under uncertainty

Abstract

A three-dimensional numerical model is developed and validated to study the effect of geometric parameters such as microchannel depth and width, manifold depth, and manifold inlet and outlet lengths on the performance of a manifold microchannel (MMC) heat sink. The manifold arrangement used to distribute the flow through alternating inlet and outlet pairs greatly reduces the pressure drop incurred in conventional fluid supply arrangements due to its shorter flow paths, while simultaneously enhancing the heat transfer coefficient by limiting the growth of thermal boundary layers. The computational analysis is performed on a simple unit-cell model to obtain an optimized design for uniform thermal boundary conditions, as well as on a porous-medium model to obtain a complete system-level analysis of multiple microchannels across one manifold. The porous-medium approach can be further modified to analyze the performance under asymmetrical heating conditions. Along with conventional deterministic optimization, a probabilistic optimization study is performed to identify the optimal geometric design parameters that maximize heat transfer coefficient while minimizing pressure drop for an MMC heat sink. In the presence of uncertainties in the geometric and operating parameters of the system, this probabilistic optimization approach yields a design that is robust and reliable, in addition to being optimal. Such an optimization analysis provides a quantitative estimate of the allowable uncertainty in input parameters for acceptable uncertainties in the relevant output parameters. The approach also yields information such as the local and global sensitivities which are used to identify microchannel width and manifold inlet length as the critical input parameters to which the outputs are most sensitive. The deterministic analysis shows that the heat transfer performance of the MMC heat sink is optimal at a manifold inlet to outlet length ratio of 3. A comparison between the deterministic and probabilistic optimization approaches is presented for the unit-cell model. A probabilistic optimization study is performed for the porous-medium model and the results thus obtained are compared with those of the unit-cell model for a uniform heat flux distribution.