Alternative Approaches to the Asymptotic Solution of ε▽ 2 u  ∂u/∂y, θ < ε ≪ 1, over a Rectangle

In the asymptotic solution of the title equation with prescribed boundary data over a rectangle 0 ≦ x ≦ ≦ ι, 0 ≦ y ≦ 1 the solution in the parabolic boundary‐layers on the side walls x = 0, l may be obtained to all orders without explicit reference to the boundary‐layers at the corners of the rectangle. Three possible methods of deriving such a solution are outlined and contrasted with the approach of Cook, Ludford and Walker [1]. The techniques described in Temperley and Todd [2] are shown to be applicable to the solution of the title problem over all parts of the rectangle. Some comments on the analogous MHD duct problem conclude the discussion.