Finite element computation of unsteady phase change heat transfer during freezing or thawing of food using a combined enthalpy and Kirchhoff transform method

摘要

An improved finite element enthalpy method was developed and implemented for solving non-linear phase change heat transfer problems such as freezing or thawing of foods with arbitrary 3D geometries. By simultaneously applying the enthalpy and Kirchhoff transforms, all non-linearities caused by the temperature-dependent thermophysical properties were incorporated in a functional relationship between the volumetric specific enthalpy and the Kirchhoff function. Such a problem reformulation results in a much more convenient solution procedure and avoids the possibility of missing the apparent specific heat capacity peak and the abrupt thermal conductivity change. Algorithms for the finite element solution of the resulting transformed equation were developed and programmed in Matlab. As the transformed equation is linear, the finite element matrices are constant and have to be calculated only once. This greatly improves the execution speed of the code, as compared to traditional finite element algorithms based on the original non-linear or enthalpy-transformed Fourier equation. As a consequence, the method is well suited for computationally intensive applications, such as numerical optimization or Monte Carlo uncertainty propagation analysis, in which typically a large number of phase change heat transfer problems must be solved. As an illustration, the freezing of a cylinder filled with tylose was investigated. A good agreement between measurements and model predictions was obtained.