ABSTRACT
Introduction .................................................................................................................................... 148 Governing Equations ...................................................................................................................... 148 Analytical Solutions ....................................................................................................................... 148
Plank’s Equation........................................................................................................................ 148 Freezing of Semi-In˜nite Region .............................................................................................. 151 Freezing of Spheres (Perturbation Solution) ............................................................................. 151
Numerical Solution: Discretizing Space ........................................................................................ 152 Finite Difference Method .......................................................................................................... 152 Finite Element Method .............................................................................................................. 154 Finite Volume Method ............................................................................................................... 156
Numerical Solution: Time Stepping............................................................................................... 157 Time Stepping in FDM ............................................................................................................. 158 Time Stepping in FEM and FVM ............................................................................................. 159
Numerical Solution: Dealing with Changes in Thermal Properties ............................................... 160 Latent Heat of Freezing ............................................................................................................. 160
Classi˜cation of Methods ..................................................................................................... 160 Effective Speci˜c Heat Methods .......................................................................................... 160 Enthalpy Methods................................................................................................................. 161 Quasi-Enthalpy Method (Temperature Correction Method) ................................................ 162
Variable Thermal Conductivity ................................................................................................. 164 Solving Food Freezing Problems with Commercial FEM Software......................................... 165
Coupled Heat and Mass Transfer ................................................................................................... 166 Mass Transfer during Freezing of Dense Foods ....................................................................... 167 Mass Transfer during Air Freezing of Porous Foods ................................................................ 168
Evaporation-Condensation Model ....................................................................................... 169 A General Model for the Freezing of Porous Foods in Air .................................................. 170
Mass Transfer during Immersion Freezing of Porous Foods .................................................... 171 Mass Transfer between Intra-and Extracellular Spaces ........................................................... 171
Supercooling and Nucleation Effects ............................................................................................. 171 High-Pressure Freezing and Thawing ............................................................................................ 174 Thermomechanical Effects during Freezing .................................................................................. 176 Conclusions .................................................................................................................................... 178 Nomenclature ................................................................................................................................. 179
Greek Letters ............................................................................................................................. 180 Subscripts .................................................................................................................................. 180 Superscripts ............................................................................................................................... 181
References ...................................................................................................................................... 181
Practical food freezing is a complex problem, involving several simultaneous physical phenomena: heat transfer, mass transfer, nucleation, crystal growth, volume change, mechanical strains, and stresses. Analytical methods can only deal with a few idealized cases, and for the vast majority of situations we must use some numerical model.
