On a linear, partly hyperbolic model of viscoelastic flow past a plate

Abstract

SynopsisThe paper presents solutions, for a class of shear relaxation functions, ofa linear problem formulated by Joseph [8] to elucidate the steady, supercritical flow of a viscoelastic fluid past a semi-infinite flat plate. The velocity (U, 0) at infinity is parallel to the plate, and‘supercritical flow ‘means that U is greater than the propagation speed C of shear waves. As a result, the vorticity satisfies a hyperbolic equation and is confined to the region downstream of a shock wave from the leading edge of the plate. The disturbance velocity fieldextends upstream of the shock and is continuous across it. In contrast to the case of a Newtonian fluid, the solutions are unique under the condition that the functions representing the vorticity on the two sides of the platebelong to a certain Banach space.