Analytical solution of a fully developed isothermal non-ideal gaseous slip flow in microchannels

In this paper, the fully developed non-ideal gaseous slip flow in circular, parallel plates, and rectangular microchannels is analyzed analytically by using Navier-Stokes equations to obtain the analytical exact solution. Van der Waals equation is used as the state equation of non-ideal gas. It is assumed that the flow is isothermal, incompressible, steady state, two-dimensional and fully developed, slip flow regime with consideration the first and second orders boundary conditions. It is developed the models for predicting the local and mean velocity, normalized Poiseuille number, and the ratio of density for the first and second orders boundary conditions. The results show that the rarefication process and Poiseuille number are a function of the Knudsen number and the cross-section geometry and Poiseuille number is independent of fluid material properties, velocity, and temperature. Also, for circular microchannel, the rarefication process occurs faster than the others.