C. Charach et B. Zaltzman, ANALYTIC MODEL FOR PLANAR GROWTH OF A SOLID GERM FROM AN UNDERCOOLED MELT, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(5), 1994, pp. 4322-4327
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.