High-performance computing systems, especially 3D ICs, are yet facing thermal exacerbation. Inter-Tier liquid cooling microchannel layers have been introduced into 3D ICs as an integrated cooling mechanism to tackle thermal degradation. Many research works optimize microchannel designs based on runtime-expensive numerical simulations or inaccurate thermofluid models. In this work, we propose accurate closed-form models on tapered microchannel to capture the relationship between channel geometry and heat transfer performance. To improve the accuracy, our correlation is based on developing flow model and derived from numerical simulation using a subset of multiple channel parameters. Our models reduce error by 57 % in Nusselt number and 45 % in pressure drop for channels with inlet width 100-400μm compared to commonly used fully developed flow based models in optimization. Obtained correlations show potential as solid foundation to achieve close to optimal design through runtime-efficient microchannel design optimization.