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Analytical solution of fully developed gaseous slip flow in elliptic microchannel. (English) Zbl 1367.76052

Summary: The paper presents an analytical solution of velocity for fully developed gaseous slip flow in elliptic micro-channels. We investigate fully developed laminar hydrodynamically steady state and incompressible slip flow with constant fluid properties. The governing equation are solved analytically for various aspect ratios using elliptic cylindrical coordinate system on applying integral transform technique to analyze gaseous slip flow in micro-channels. Prior to apply integral transform technique, Arfken transform was used on momentum equations and first-order slip boundary conditions at each channel walls were imposed. Based on the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The results of a normalized Poiseuille number \((Po)\) for elliptic micro-channels show very good improvement with the previous results of rectangular and elliptic microchannels. Further, it is also observed that the present values of friction factor and Reynolds number product \((fRe)\) shows good agreement for smaller aspect ratios \((\varepsilon)\).

MSC:

76N15 Gas dynamics (general theory)
76R10 Free convection
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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