On Similar Solutions of the Steady Quasi-two-dimensional Incompressible Laminar Boundary-layer Equations

Abstract

Using the orthogonal curvilinear coordinates, three-dimensional incompressible laminar boundary-layer equations are obtained. These equations reduce to two-dimensional type, if one component of the velocity and the pressure gradient in that direction are negligible throughout the boundary layer.
Conditions for the existence of similar solutions for such quasi-two-dimensional boundary layer are investigated. New similar solutions are found using “planar coordinates” α, β, γ (γ=0 gives the surface) in the case where the velocity at the outer edge of the boundary layer is expressed as {B₁G(α, β)+B₂}^m or B₂exp {B₁G(α, γ)}, where m is a constant, B₁ and B₂ are arbitrary functions of β, and G(α, β) is a known function determined by the surface geometry.