In this work, we extend a numerical tool capable of solving compressible and incompressible gas flows to study the momentum and heat transfer rates in micro/nano channels with high aspect ratio (L/H = 8000), where the compressibility effect is dominant. The constant heat flux thermal boundary condition is firstly applied at the wall. Next, the flow regime is extended to the early transition regime employing a high order slip velocity boundary condition based on the kinetic theory assumptions. The accuracy of the present results in the slip flow regimes is evaluated against other available theoretical and experimental results. The thermal and compressibility effects on the pressure and Knudsen number distribution are extensively studied along the channel at early transition regimes up to Kn = 0.5. Likely, this Knudsen is the highest one to be reached via applying the foregoing boundary conditions.

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