Modeling of Rectangular Microchannel Heat Sink with Non-Uniform Channels and Multi-Objective Optimization

Rectangular microchannel heat sinks (MCHS) are widely used to cool high-heat-flux electronic devices. However, previous studies focused mainly on MCHS with uniform channels (UCs). This study considers a microchannel heat sink with non-uniform channels (NUCs). A mathematical model is developed based on energy equations and the Darcy flow principle. Explicit expressions for total thermal resistance and coolant pressure drop are derived using the thermoelectric analogy. Experiments and numerical simulations are performed to verify the mathematical model. As non-uniformity increases, total coolant pressure drop decreases but at the cost of higher thermal resistance. The overall performance of NUCs is better than that of UCs because of their lower ratio of pumping power to cooling power. Heat transfer performance of NUCs changes little for more than 120 channels and depends mainly on channel arrangement. A multi-objective optimization is conducted to minimize the thermal resistance and pumping power of an NUC. An optimal NUC saves 64% pumping power compared with a conventional UC for the total thermal resistance of 0.1 degrees C/W, indicating that the use of non-uniform channels could be very helpful to reduce the flow resistance of MCHS.