# CODES FOR "HYBRID INTEGRAL TRANSFORM ANALYSIS OF SUPERCOOLED DROPLETS SOLIDIFICATION"

*Version: Wolfram Mathematica 12.0.0.0 Student Edition*

*Platform: Mac OS X x86 (64-bit)*

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

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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 đ_{o}, 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 (*L _{e}*)
also needs to be substituted by the latent heat of sublimation (

*L*). Also, solid state correlations for đ

_{sb}_{v}and đ

_{â}must be used.

Equationâs number mentioned in comments throughout the code refers to the equationâs number from the text.

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

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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.

Equationâs number mentioned in comments throughout the code refers to the equationâs number from the text.