Matched asymptotic solution for the solute boundary layer in a converging axisymmetric stagnation point flow

A novel boundary-layer solution is obtained by the method of matched asymptotic expansions for the solute distribution at a solidification front represented by a disk of finite radius R₀ immersed in an axisymmetric converging stagnation point flow. The detailed analysis reveals a complex internal structure of the boundary layer consisting of eight subregions. The development of the boundary layer starts from the rim region where the concentration, according to the obtained similarity solution, varies with the radius r along the solidification front as ∼ln^1/3(R₀/r). At intermediate radii, where the corresponding concentration is found to vary as ∼ln(R₀/r), the boundary layer has an inner diffusion sublayer adjacent to the solidification front, an inner core region, and an outer diffusion sublayer which separates the former from the outer uniformly mixed region. The inner core, where the solute transport is dominated by convection, is characterized by a logarithmically decreasing axial concentration distribution. The logarithmic increase of concentration along the radius is limited by the radial diffusion becoming effective in the vicinity of the symmetry axis at distances comparable to the characteristic thickness of the solute boundary layer.