Version: Wolfram Mathematica 12.0.0.0 Student Edition

Platform: Mac OS X x86 (64-bit)

Code 1: RSPA-2020-0874R1_Cooling stages.nb

This file contains the code for cooling stages calculation. This particular case is the calculation of the supercooling stage (or liquid cooling), but it can be easily adapted to calculation of the cooling stage (or solid cooling). However, the thermophysical properties of the liquid phase need to be changed by the properties of the solid phase. Also, the initial temperature distribution, which for the supercooling stage (stage 1) is the uniform temperature 𝑇o, for the cooling stage (stage 4) it becomes the spatially varying temperature distribution in the droplet at the end of the solidification stage. Since the droplet is solid in this stage, convective mass transfer occurs not through evaporation, but through sublimation, and therefore the latent heat of evaporation (Le) also needs to be substituted by the latent heat of sublimation (Lsb). Also, solid state correlations for 𝜌v and 𝜌∞ must be used.

Equation’s number mentioned in comments throughout the code refers to the equation’s number from the text.

Code 2: RSPA-2020-0874R1_Freezing stage.nb

This file contains the code for freezing stage calculation. This particular case is the calculation of the freezing stage for the hypothesis of a uniform distribution of the initially formed ice, but it can be easily adapted to calculation of the spherical cask hypothesis by the use of equations 37.a and 37.b described in the text.

Equation’s number mentioned in comments throughout the code refers to the equation’s number from the text.