Analytical Solutions to the Boundary Integral Equation: A Case of Angled Dendrites and Paraboloids

Abstract

The boundary integral equation is solved analytically in the case of two- and three-dimensional growth of angled dendrites and arbitrary parabolic/paraboloidal solid/liquid interfaces. The undercooling of a binary melt and the solute concentration at the phase transition boundary are found. The theory under consideration has a potential impact in describing more complex growth shapes and interfaces. © 2020 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.