Constructal cooling channels for micro-channel heat sinks

This paper documents the geometric optimisation of a three-dimensional micro-channel heat sink. The objective is to minimise the peak temperature from the walls to the coolant fluid. The optimisation is performed numerically by using the finite volume method. The numerical simulation was carried out on a unit cell with volume ranging from 0.1 mm3 to 0.9 mm3 and pressure drop between 10 kPa and 75 kPa. The axial length of the micro-channel heat sink was fixed at 10 mm. The cross-sectional area of the micro-channel heat sink is free to morph with respect to the degree of freedoms provided by the aspect ratio and the solid volume fraction. The effect of the total solid volume fraction and the pressure drop on the aspect ratio, channel hydraulic diameter and peak temperature is investigated. The numerical results show that the degrees of freedom have a strong effect on the peak temperature and the maximum thermal conductance. The optimal geometric characteristics obtained numerically (the aspect ratio and the optimal channel shape (hydraulic diameter)) are reported and compared with those obtained from approximate relationships using scale analysis. The predicted trends are found to be in good agreement with the numerical results.