Perturbation Solutions for the Shape of a Solidification Interface Subjected to a Spatially Periodic Heat Flux

Abstract

In the manufacture of certain high-technology materials (such as strengthened composites for turbine and compressor blades) from a melt, it is essential to control the heat transfer conditions in such a way that a planar solidification interface is maintained within a given tolerance. Spatial nonuniformities in the heat flux imposed along the solidification interface may cause deformation. In this paper we analyze the interfacial shapes resulting from a periodic heat flux variation along the interface. Two cases of practical interest are examined. In case (a) the amplitude of heat flux variation is assumed small compared to the mean value, and in case (b) the wavelength of the imposed heat flux variation is considered to be much larger than a characteristic length in the transverse direction. In both cases, sensitivity of the interface shape with respect to heat flux nonuniformities is also determined.