Based on the constructal theory concepts, an investigation is carried out to optimize circular multilayer microchannels embedded inside a rectangular heat sink with different numbers of layers and flow configurations. The lower surface of the heat sink is uniformly heated, while both pressure drop and length of the microchannel are fixed. Also, the volume of the heat sink is kept fixed for all studied cases, while the effect of solid volume fraction is examined. All the dimensions of microchannel heat sinks are optimized in a way that the maximum temperature of the microchannel heat sink is minimized. The results emphasize that using triple-layer microchannel heat sink under optimal conditions reduces the maximum temperature about 10.3 °C compared to the single-layer arrangement. Further, employing counter flow configuration in double-layer microchannel improves its thermal performance, while this effect is less pronounced in the triple-layer architecture. In addition, it is revealed that the optimal design can be achieved when the upper channels of a multilayer microchannel heat sink have bigger diameters than the lower ones. Finally, it is observed while using two layers of microchannels is an effective means for cooling improvement, invoking more layers is far less effective and hence is not recommended.

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