Fully-developed laminar flow in sinusoidal grooves

The flow of a constant property fluid through a sinusoidal groove has been analyzed. A numerical solution of the conservation of mass and momentum equations for fully developed flow is presented. The mean velocity, volumetric flow rate, and Poiseuille number are presented as functions of the groove geometry, meniscus contact angle, and shear stress at the liquid-vapor interface. In addition, a send-analytical solution for the normalized mean velocity in terms of the normalized shear stress at the meniscus is shown to agree with the numerical data quite well.