Analytical solution in parametric form for the two-dimensional liquid jet of a power-law fluid

Abstract

The two-dimensional liquid jet of a power-law fluid is considered. The problem is formulated in terms of the components of fluid velocity which satisfy the continuity equation and the momentum boundary layer equation for a power-law fluid. The multiplier method is used to investigate the conservation laws for the system of partial differential equations and a conserved vector and the corresponding conserved quantity for the two-dimensional liquid jet is derived. The Lie point symmetries of the system of partial differential equations are calculated. A linear combination of the Lie point symmetries is associated with the conserved vector for the liquid jet to obtain the associated Lie point symmetry which is used to generate the invariant solution. An analytical solution in parametric form for the liquid jet is derived. It is found that a solution for the liquid jet exists only for 1/2<n<∞ where n is the power law exponent. The profile of the free surface and the thickness of the liquid jet are compared for a shear thinning fluid with 1/2<n<1, a Newtonian fluid with n=1 and a shear thickening fluid with 1<n<∞.