Analytical solution in parametric form for the two-dimensional liquid jet of a power-law fluid. (July 2017)

• Record Type: Journal Article
• Authors: Magan, A.B.; Mason, D.P.; Mahomed, F.M.
• Is Part Of: International journal of non-linear mechanics. Volume 93(2017)
• Page Start: 53
• Page End: 64
• Publication Date: 2017-07
• Subjects: Two-dimensional liquid jet -- Power-law fluid -- Conservation laws -- Conserved quantity -- Lie point symmetry -- Invariant solution; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2017.05.001
• Languages: English
• ISSNs: 0020-7462

Abstract

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 < ∞ . Abstract : Highlights: Analytical solution in parametric form for a liquid jet of a power-law fluid. Conserved quantity is obtained only from the continuity equation. Solution generated by Lie point symmetry associated with conserved vector. Solutions with fluid outflow from a point source exist only for 1 / 2 < n < ∞ . Shape of the free surface and the width of the jet depend on power-law exponent n.