The motion induced between a rotating plate and a radially stretching or shrinking plate

The flow induced between parallel plates separated by a distance h executing different types of in-plane motion is investigated. The upper plate radially stretches at strain rate a and the lower plate rotates at angular velocity Ω about a common axis. A similarity solution form reduces the Navier-Stokes equations to a coupled pair of ordinary differential equations in two parameters: R = |a| h2/ν and σ = Ω/|a|, where ν is the kinematic viscosity of the fluid. Solutions are obtained for both stretching and shrinking upper plates and numerical results for pressure gradient and wall shear stress parameters are found and compared with low-R series solutions and large-R asymptotic behaviors. Sample radial and azimuthal velocity profiles reveal regions of zero radial and azimuthal wall shear stress which are studied in detail. This work represents the first study of the flow induced between parallel plates for which each plate executes a different type of in-plane motion.