Heat transfer with a moving boundary—application to transient solidification of a warm liquid on a moving cold plate

Abstract

The problem of moving boundary encountered in the freeze coating of polymeric melt on nonisothermal limited heat capacity moving metallic cold plate is presented. The transient convective heat transfer from polymeric melt to the frozen layer on the plate and the transient axial variation of the plate temperature due to the change of the plate thermal capacity are modeled. The governing differential equations are transformed in terms of dimensionless quantities. It was found that the process is governed by two partial ditterential equations and one ordinary differential equation. The process governing equations are solved numerically. Finite element method is used to solve the partial differential equations and Runge—Kutta method is used to solve the ordinary differential equation. The history of the axial variation of the shape of the freeze-coat is presented. The system controlling parameters are identified. The effect of the controlling parameters on the freeze-coat thickness is studied and presented in graphs.