Steady and unsteady exact inverse solutions for the flow of a viscous fluid

Abstract

In this paper, inverse solutions are derived for the equations of two dimensional flows of a viscous incompressible fluid by assuming certain conditions on the stream function. The equation is coupled in terms of the stream function by eliminating the pressure between the component forms of the flow equation. The solutions for steady and unsteady cases are found by prescribing the vorticity proportional to the stream function perturbed by the uniform stream in x and y directions. The solutions for the stream functions and velocity components are derived in each case and comparison of results have been made with the known results. Key words: Inverse solutions, viscous fluid, unsteady flow, stream function.