Numerical evaluation of temperature profiles and interface position in filaments undergoing solidification

A numerical method has been described for the solution of the general equations which depict solidification in the cylindrical coordinate system. The method has been outlined for cooling and solidification of a moving filament of molten polymer. The solution is given in terms of six dimensionless variables: α l /α s , k l / k s , hR / k R , L /[ C ps ( T o − T c )], T o / T c , and σϵ p R ( T o − T c ) 3 / k R . Plots are shown for the solution of the heat transfer equations and associated boundary conditions for several values of the dimensionless variables. The method describes the process of cooling and freezing liquids when convective and/or radiative energy losses are considered. The form of the theoretical equation compares very favorably with experimental data.