Analytical Solution of Non-ideal Gaseous Slip Flow in Circular Sector Micro-channel

AbstractAnalytical solutions of gaseous slip flow in a microchannel with different cross-sections play an important role in the understanding of the physical behavior of gases and other phenomena related to it. In this paper, the fully developed non-ideal gaseous slip flow in circular sector microchannel is investigated using the conformal mapping and the integral transform technique to obtain the analytical exact solution. Van der Waals equation is used as the equation of state for a non-ideal gas.It is developed the models for predicting the local and mean velocity, normalized Poiseuille number,and the ratio of density for conditions where the small radius of the circular sector cross-section is zero (r۱*→۰) and is the opposite of zero (r۱*≠۰, r۱*=۱۰µm).Rarefication process and effects of wall slippage are important physical phenomena that are studied. The results show that the rarefication process depends on Knudsen number, and cross-section geometry. In order to validate the analytical solution, the results of the problem are compared to the analytical and numerical solutions. Good agreement between the present study and other solutions has confirmed.

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Keywords: Slip flow ، Microchannel ، Circular sector ، Integral transform ، Conformal mapping