Annular axisymmetric stagnation flow on a moving cylinder

Fluid is injected from a fixed outer cylindrical casing onto an inner moving cylindrical rod. Using similarity transform, the Navier–Stokes equations reduce to a set of nonlinear ordinary differential equations, which are integrated numerically. Asymptotic solutions for large and small cross-flow Reynolds numbers and small gap widths are also found. Drag, torque and heat transfer on the moving rod are determined. The problem is particularly important in pressure-lubricated bearings.