Linearized solution of quasi-steady Stefan problem in vertical gradient freeze configuration

The present paper deals with a shape of a sharp phase boundary under conductivity controlled quasisteady solidification in a long cylinder with a given surface temperature and growth velocity. An approximate analytical closed form solution is obtained linearizing the Stefan problem in a neighbourhood of the practically desirable planar interface. The relative error of the solution is evaluated numerically and shown below 15% for reasonable interface depths (1/2 of the crystal radius) and desreasing linearly (or more rapidly) as interface deformation decreases.