Hot spot temperature optimization of micro-channel heat sinks enabled by designing vortex generators and realizing optimal flow pattern

Reduction of hot spot temperature is critical for electronic devices under high heat flux conditions. Micro-channel heat sinks (MCHSs) are commonly used in electronic cooling, with vortex generators introduced to enhance the heat transfer. However, existing convective heat transfer optimization equations are not consistent with the aim of hot spot temperature minimization, which are not efficient for design of vortex generators in MCHSs. To address this issue, the optimization equations with minimizing the hot spot temperature of MCHSs are developed, and a novel method is proposed to efficiently design vortex generators in MCHSs. The heat convection optimization equations aiming at hot spot temperature minimization of MCHSs under fixed power consumption are derived using variational method. The equations enable us to achieve the optimal flow field that guarantees a lower hot spot temperature than those obtained based on equations that aim at entropy generation minimization or entransy dissipation extremum in previous studies. The results reveal that the mechanism of hot spot temperature minimization in the rectangular channel is to induce four longitudinal vortices at the cross-section with specific rotations that drive more fluid to the heating surface. Furthermore, vortex generators composed of the inclined triangular-prism ribs and plates are inserted into the channel, which successfully constructs the optimal flow patterns matching the derived optimization equations. The generated similar longitudinal vortices are evidenced by numerical results. With mass flow rate at 0.1 g/s, the hot spot temperature of the MCHSs with the designed vortex generators is reduced by 32.7 K, and the maximum temperature rising decreases by 48 %, and the performance evaluation criterion increases by 60 % when compared to the channel without vortex generators. Moreover, the designed vortex generator increases the performance evaluation criterion by more than 55 % compared to the one in the previous study under different Reynolds numbers. The developed optimization equations provide valuable insights of the optimal flow field which aims at reducing hot spot temperature, and the proposed method based on the optimal flow field shows great potential for efficient design of vortex generators in MCHSs for performance improvement.