ON THE EVOLUTION OF UNSTEADY DISTURBANCES IN CONTINUOUS STRIP CASTINGPROCESSES

Continuous solidification processes in thin layers of molten metal are of central importance in many fields of modern metallurgical engineer ing. This paper deals with unsteady disturbances possibly emerging at the free surface or the phase boundary within the solidification zone of a horizontal strip casting process. Assuming that the wave lengths of the disturbances are large compared to the characteristic depth of the melt, we can apply governing equations for one-dimensional flow. F urthermore, we assume the amplitudes of the disturbances to be so smal l that their evolution can be regarded as weakly nonlinear. Since unst eady wave propagation phenomena can arise from temperature variations as well as from the excitation of waves at the free surface or the sol idification front, both mechanisms will be studied in the following. I n the latter case the disturbances at the surface are found to be gove rned by the inviscid Burgers equations with varying coefficients and w ill then, in general, develop shock discontinuities. (C) 1997 American Institute of Physics. [S1070-6631(97)02112-0].