Asymptotic analysis of surface waves in continuous strip casting processes

This paper presents a two-dimensional analysis of surface waves possibly em erging in a specific open channel flow with continuous solidification, i.e. the fluid consisting of molten material is cooled from below and solidifie s. In modem metallurgical engineering such processes are of importance for the strip casting of steel and other metals. The study is based on the assu mption that the wavelengths are large compared to the characteristic depth of the melt but small compared to the solidification length. Within the fra mework of a weakly nonlinear theory the use of the Euler equations suppleme nted with the appropriate boundary conditions at the solidification front a nd the free surface yields two Korteweg-de Vries equations with varying coe fficients, which govern the propagation of the waves. However, the adopted form of the asymptotic expansions ceases to be valid as the point of comple te solidification is approached, where the displacements at the free bounda ry and the depth of the melt are of the same order. Thus, a separate invest igation for this region is carried out in order to describe the further evo lution of the surface waves and its influence on the final shape of the ful ly solidified metal sheet. (C) 2000 The Japan Society of Fluid Mechanics an d Elsevier Science B.V. All rights reserved.