The linearly stretching wall jet

Abstract

Abstract It is constructed a set-up comprising a jet from a slit at the leading edge, discharged over a linearly stretching wall. The non-similar flow can be interpreted as a combination of two distinct similarity regions; Akatnow–Glauert flow at the leading edge and Crane flow far away from it. In this respect, it is employed appropriate coordinate expansions to explore perturbatively the behavior of the flow near the similarity regions. A suitable composite transformation amalgamated with an abridgmentof the stream-wise coordinate, facilitated an immaculate numerical simulation of the involved nonlinear partial differential equation over the entire spatial domain ( 0 ≤ X ∞ , 0 ≤ η ˆ ∞ ) followed by quasi-linearization technique together with an implicit algorithm of a tridiagonal form. As a result, shear stress at the wall is accurately predicted through a proposed formulation, valid all the way along the wall. It is also exhibited that there exists a transition region with a critical coordinate in the stream-wise direction in which the shear stress at the wall becomes zero. This universal coordinate (namely, the turning point) is determined as, reasonably close to, X c r. ≈ 13 23 ( X is a dimensionless coordinate measuring distance along the wall and η ˆ is the dimensionless non-similarity variable).