Application of Point Matching Techniques to Two-Dimensional Solidification of Viscous Flow Over a Semi-Infinite Flat Plate

Abstract

An analytical method is presented for the solution of two-dimensional solidification of fluid in motion over a semi-infinite plate. The method is applicable to other two-dimensional free boundary problems involving convection of the liquid phase. The solution is based upon an instantaneous source method which transforms the moving free boundary problem to a stationary domain. The transformed problem is solved by a Laplace transformation which results in a two-dimensional elliptic problem in an irregularly shaped region. An approximate point matching method is employed to solve the elliptic problem. Interface motion is obtained from the solution of a nonlinear integrodifferential equation of the Volterra type. Numerical solutions are presented to verify the validity of the model used in the analytical method and to examine the accuracy of the analytical solution.