Instability of Navier slip flow of liquids

Investigation of the entrainment of gases induced by a surface wave propagating along the wall of a microtube is conducted by using a relaxed model with slip velocity boundary conditions. Flow patterns tuned by critical reflux values ${a}_{0}$, Knudsen numbers, Reynolds numbers, and the wave number are demonstrated. Results show that once the cross section of the microtube is narrowed down (slip velocity increasing) there are earlier backward flows and the flow pattern is much more complicated. Our results should be useful for the design of micro total analytical systems.

Transport control within a microtube.

Vectored Injection into Laminar Boundary Layers with Heat Transfer

The results of a systematic study of self-similar solutions of the Blasius equation are presented for a wide range of both normal and tangential surface injection velocities. Only flows with non-vanishing shear are considered; however, an arbitrary orientation of the injection vector is allowed. It is found that a positive tangential component of injection (downstream vectoring) significantly increases the mass transfer rate required to blow off the boundary layer. For upstream vectoring, a new group of solutions is found over a certain range of the tangential wall velocity wherein the wall shear is doublevalued.

Vectored Injection into Isobaric Laminar Boundary Layer Flows

Numerical results obtained by solving the complete system of Navier-Stokes equations for a channel with one movable surface are evaluated.

Flow analysis in a channel with a moving wall

A method is developed to solve the two‐dimensional incompressible laminar boundary layer with mass transfer and slip at the surface. The properties of the injected gas are assumed the same as those of the main flow. The velocity distribution is nonsimilar in the flow direction and is obtained by a series expansion in terms of a mass transfer parameter e(S) and a slip parameter σ(S). Results are presented for various combinations of the two parameters. The validity of the method is verified by comparison with a momentum integral type solution over a range of values of the two parameters.

Richard C. Lind

Papers

Laminar Boundary Layer with Mass Transfer and Slip