Optimization Under Uncertainty of Manifold Microchannel Heat Sinks

Abstract

Conventional microchannel heat sinks provide good heat dissipation capability but are associated with high pressure drop and corresponding pumping power. The use of a manifold system that distributes the flow into the microchannels through multiple, alternating inlet and outlet pairs is investigated here. This manifold arrangement greatly reduces the pressure drop incurred due to the smaller flow paths, while simultaneously increasing the heat transfer coefficient by tripping the thermal boundary layers. A three-dimensional numerical model is developed and validated, to study the effect of various geometric parameters on the performance of the manifold microchannel heat sink. Apart from a deterministic analysis, a probabilistic optimization study is also performed. In the presence of uncertainties in the geometric and operating parameters of the system, this probabilistic optimization approach yields an optimal design that is also robust and reliable. Uncertainty-based optimization also yields auxiliary information regarding local and global sensitivities and helps identify the input parameters to which outputs are most sensitive. This information can be used to design improved experiments targeted at the most sensitive inputs. Optimization under uncertainty also provides a quantitative estimate of the allowable uncertainty in input parameters for an acceptable uncertainty in the relevant output parameters. The optimal geometric design parameters with uncertainties that maximize heat transfer coefficient while minimizing pressure drop for fixed input conditions are identified for a manifold microchannel heat sink. A comparison between the deterministic and probabilistic optimization results is also presented.