Compact modeling of fractal tree-shaped microchannel liquid cooling systems

Demands for higher computational speed and miniaturization have already resulted in extremely high heat fluxes in microprocessors. Fractal tree-shaped microchannel liquid cooling systems are novel heat transfer enhancement systems to keep the temperature of the microprocessors in a safe range. Due to the complexity of these systems, their full field numerical modeling for simulation of the flow and temperature fields is too time consuming and costly, particularly to be used within iterative optimization algorithms. In this paper, a quick but still accurate compact modeling approach based on Flow Network Modeling (FNM) is introduced for analysis of the flow filed in fractal microchannel liquid cooling systems. The compact method is applied to a representative fractal microchannel cooling system and the obtained velocity and flow rate distribution are validated against a full Computational Fluid Dynamics (CFD)-based model for three different designs. The compact model shows good agreement with the CFD results and robustness on different designs, while requiring much less computational capability and time. Afterwards, the compact model is used for optimization of the geometry of the fractal cooling system to achieve maximum flow rate and uniform flow distribution among the channels for a fixed pressure drop.