ANALYTIC MODEL FOR PLANAR GROWTH OF A SOLID GERM FROM AN UNDERCOOLED MELT

Planar growth of a solid germ of infinitesimal initial thickness from an undercooled melt is addressed within a continuum model with linear interfacial kinetics. For this problem, we present an analytic solutio n that describes the global features of the process beyond the initial and long-time limits. In particular, it yields analytic expressions f or the main characteristics of the transient regime. This solution is obtained within the heat balance integral method with a relatively sim ple boundary layer approximation for the temperature profile in the me lt. The analytic solution is validated by the known asymptotic results , as well as by comparison with the numerical solution of the problem considered. The emerging physical picture is formulated in terms of th e evolution characteristics of the phase-change front and those of the thermal boundary layer.