http://worldcat.org/entity/work/id/137282355

Flow through a cylindrical tube in the slip flow regime

By the introduction of a parabolic velocity profile, the boundary layer momentum and continuity equations were reduced to ordinary differential equations by integration across the tube. The coefficients in the velocity profile were determined to satisfy the slip boundary condition of Maxwell at the tube wall and the condition of zero shear at the edge of the boundary layer. In place of the energy equation, the total temperature in the inlet region was assumed to be a linear function of the velocity and the constants were determined to satisfy the temperature jump condition of Poisson at the wall. Similar formulae were developed for isothermal flow. Calculations of the inlet length for the flow to become fully developed viscous slip flow were made for both theories. For inlet Mach numbers above a critical value at small dimensionless inlet mean free paths, the flow does not become fully developed but the boundary layer thickness attains a maximum when the core velocity is about equal to the speed of sound. This critical Mach number increases rapidly with increasing inlet values of the mean free path, indicating that slip flow is more apt to become fully developed than continuum flow. (Author).

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