Wavy Viscous Flow in a Plane Channel: Stability and Heat Transfer from the Walls

Using the full Navier–Stokes equations, two branches of viscous fluid flow regimes were found in the form of steady-state traveling waves between two smooth surfaces. On the plane of parameters (wavelength, Reynolds number), the region of existence of the new solutions is determined and it is shown that the flow regimes corresponding to one of the branches are unstable. Stable regimes exist over a wide range of Reynolds numbers, starting from values significantly lower than the Reynolds number at which the linear stability of the basic steady-state solution is lost. The key wave characteristics of the new types of solutions are calculated. Implementing these solutions requires a pressure gradient significantly greater than that required to obtain the basic steady-state solution, resulting in more intense heat transfer from the walls.