Numerical Optimization of an Array of Triangular Microchannels using Constructal Theory

In the present study, an arrangement of triangular microchannels with different contact angles is analyzed and optimized following the guidelines provided by the constructal theory to reach to the maximum heat removal rate. This investigation is performed analytically and numerically. Based on the obtained results, it is emerged that this optimization is independent of the number and the type of the arrangement of the microchannels. It is also observed that increasing the pressure drop through the triangular microchannels decreases the optimal hydraulic diameter. Numerical results recommend that the microchannel with contact angle of 60° possesses the highest heat transfer rate at a given pressure drop, and decreasing the contact angle of the triangular cross-section leads to lower heat transfer rates. Comparing the analytical and numerical results of the optimal hydraulic diameter of the microchannel heat sinks, a reasonable agreement is observed; however, due to some assumptions which are considered at the analytical method, the analytical predictions of the configurations having the highest heat transfer rate are inaccurate. Therefore, the numerical optimization should be used to choose the configuration with the highest cooling capacity.