In spite of the various aspects of thermal-aware designs in 3D IC, the thermal barrier is yet to overcome to enable the technology. As liquid cooling microchannel is highly effective means in thermal management, it has been rising as a promising technique to integrate into 3D IC. To attain the feasibility, it is crucial to design low-power and highly-efficient microchannel in compact chip packaging. In this work, we derive complete closed-form correlations which accurately model converging, diverging and uniform microchannels. We use microchannel designs of width 10-600 μm, tapering angle of -11-20° with Reynolds number of 39-99, inlet volumetric flow rate of 10- 8 m3/s and heat flux of 100 W/cm2 for the derivation. Then, we optimize the microchannel design to maximize the thermal performance while constraining pumping power and channel widths. Optimization is based on our derived correlations for heat transfer and pressure drop and the resulting microchannel designs are validated with numerical simulations. Temperature maps of the optimized channels from numerical simulation demonstrate accurate estimation of overall thermal resistance and proves the reliability of the optimization.