I wish to model an object with an internal heat source melting through antarctic ice. The equilibrium temperature of this ice would be well below freezing, which I intuitively suspect makes the problem a bit harder.

Apparently my question was unclear: A source of constant heat output exists inside an object. It starts on a bed of very cold ice and (hopefully) melts through it. I want to model that. What software can do that fairly easily?

  • Are you looking for a numerical model of a 3D graphical tool? – Steve Barnes Jun 17 '17 at 7:18

It sounds like a suitable problem for Calculix possibly controlled via pyCalculix.

You need to keep in mind several phase changes:

  1. Initially only the base of the heat source will be in contact with ice, (at the low starting temperature), warming the ice it is in contact with which effectively has an infinite thermal sink, so the heat will be defusing with the thermal transmission of ice and, assuming perfect coupling, warming the ice at based on the specific heat of ice - worse this changes significantly with temperature 24.8 J/(mol K) at −100 °C, 32.77 J/(mol K) at −38.3 °C, 37.84 J/(mol K) at −2.2 °C.
  2. Once the ice immediately in contact with the point of contact reaches 0 degrees C you will have to take into account the specific heat of melting ice to water.
  3. As the body sinks proportionally more of it will be in contact with the water, which will be in contact with the ice, so you will get better transfer.
  4. As it sinks further there will be a water column above removing heat by convection, (and possibly evaporation).
  5. When it sinks far enough the water in the column above will start to freeze, removing any evaporation component.
  6. As the pressure grows the melting point of the ice drops slightly but I suspect that this will be negligible.
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