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Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates

By Rana Khalid Naeem, Asif Mansoor and Waseem Ahmed Khan


Abstract—The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the ( ξ, ψ) − or ( η, ψ)- coordinates where ψ ( x, y) �is the stream function, ξ �and η �are the parts of the analytic function, ϖ = ξ ( x, y) + iη( x, y). Most of the solutions involve arbitrary function / functions indicating that the flow equations possess an infinite set of solutions. Keywords—Exact solutions, Fluid of variable viscosity, Navier-Stokes equations, Steady plane flow

Year: 2013
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