Boundary layer flow for a moving belt

A similarity solution for an ordinary third-order differential equation with a physical interpretation is presented for a boundary layer flow over a moving flat plate. Specifically, a pair of moving belts over two pulleys located at the origin of a system of planar Cartesian coordinates is used to illustrate the problem of a rotating cylinder in a cross flow. A sequence of approximations is given to parameterize the flow. It is noted that the stream lines remote from the belt are displaced inward toward the surface rather than outward, and that a standing eddy arises in cases for which the free stream moves in a direction opposite to that of the belt's motion.