The present work investigates the extension of Navier–Stokes equations from slip-to-transition regimes with higher-order slip boundary condition. To achieve this, a slip model based on the second-order slip boundary condition was derived and a special procedure was developed to simulate slip models using FLUENT®. The boundary profile for both top and bottom walls was solved for each pressure ratio by the customized user-defined function and then passed to the FLUENT® solver. The flow characteristics in microchannels of various aspect ratios (a = H/W = 0.002, 0.01, and 0.1) by generating accurate and high-resolution experimental data along with the computational validation was studied. For that, microchannel system was fabricated in silicon wafers with controlled surface structure and each system has several identical microchannels of same dimensions in parallel and the processed wafer was bonded with a plane wafer. The increased flow rate reduced uncertainty substantially. The experiments were performed up to maximum outlet Knudsen number of 1.01 with nitrogen and the second-order slip coefficients were found to be C1 = 1.119–1.288 (TMAC = 0.944–0.874) and C2 = 0.34.

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