Two-dimensional compressible momentum equations were solved by a perturbation analysis and the PISO algorithm to investigate the effects of compressibility and rarefaction on the local flow resistance of isothermal gas flow in circular micro-channels.The computations were performed for a wide range of Reynolds numbers and inlet Mach numbers.The explicit expression of the normalized local Fanning friction factor along the microchannel was derived in the present paper.The results reveal that the local Fanning friction factor is a function of the inlet Mach number,the Reynolds number and the length-diameter ratio of the channel.For larger Reynolds and inlet Mach numbers,the friction coefficient in the microchannel is higher than the value in a macrotube,and the gas flow in the microchannel is dominated only by compressibility.For smaller Reynolds and inlet Mach numbers,the Fanning friction factor of gas flow in the microchannel is lower than that in a circular tube of conventional size due to slip flow at the wall and thus,rarefaction has a significant effect on the fluid flow characteristics in a microchannel.
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