An asymptotic analysis for directional solidification of a diffusion-dominated binary system

Asymptotic solutions for a time-dependent, axisymmetric directional solidification system

“…The discussions in Refs. [13,22,24] indicate that the choice of scaling is dictated by the size of the concentration gradient at the solidification front and the influence of solute concentration on the interface temperature. The scaling Oð 2 Þ is appropriate for systems with small gradient or small influence of concentration on the interface temperature.…”

“…This problem was identified in Ref. [22]. Hence, it is important that the surface free energy g is not set to 0 in order to capture the dynamic transition as aðtÞ changes sign.…”

“…[13] were obtained in the context of a uniform ambient temperature (heater) profile. More recently, Haldenwang and Guerin [18] and Kupchella et al [22] used similar assumptions to define a non-ideal furnace and examine the transverse thermal effects that arise due to axially varying heater profiles and nonadiabatic sidewall conditions. The goal of this paper is to combine the quasisteady approach of Clemons et al [21] with the twodimensional approach of Brattkus and Davis [13].…”