Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.