Heat transfer to ice under vacuum

[a991088]

Hello all,
I am trying to solve a sublimation/heat transfer problem and could use some help from you.
I have a freeze dryer under vacuum at a pressure of say 0.1 mbar. The temperature of the ice in the dryer is say -20 degree centigrade (253 Kelvin). To assist sublimation, I am providing heat to the stainless steel jacket wall of the dryer at say 30 degree centigrade (303K).
The jacket area is 3 m2

Now I would like to increase the temperature of the jacket wall to 40 degrees (313 K). How can I determine what the new ice temperature will be?

 

[EdStainless]

Since you are in a vacuum radiant heat transfer is all that you have.
Take the equation that you used for the first case and substitute the new wall temp.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[a991088]

Hi EdStainless,
Thanks for your response
The first value are assumptions of the state of the system and not calculated - so I have no equation.
Secondly, I feel conduction from the wall to the ice is the dominant heat transfer mechanism and radiation is minimal. The ice is in contact with the wall.

 

[EdStainless]

Then set up the conduction formula and adjust eh constants until it matches your current situation.
In my experience the ice that forms in these is very low density and has poor heat transfer properties, it is almost an insulator.
But you should be able to estimate an increase in Q and the resulting temps.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[MortenA]

Unless you change the pressure then the temperature of the ice will not change (it seems like a schoolbook trick question) but your evaporation rate will. Im uncertain what the vacuum will actualæly do to the temperature of the dry ice. Of course CO2 acnnot exist at vacuum (only solids can water would also evaporate) and unless the vapours are removed (by a vacuum pump) then then pressure will go up. BUT assuming that the gas is removed what is the surface temperature then? At a low pressure say 100 Pa CO2 will go from solid to gas at -140ºC so the ice at the surface will have this temperature - but thats not vacuum - its just a low pressure. So i guess i would say - surface is -140ºC and the rest of the ice will most likely have a similar temperature assuming good heat conduction

 

[chicopee]

It is more about molecular diffusion than heat transfer if you have an open system instead of a closed one.

 

[a991088]

Thanks MortenA & Chicopee,
I agree that the pressure and ice temperature are coupled and I have a vacuum pump to remove the vapour.
My feeling about the whole process is that the increase in temperature of the steel jacket will lead to an increase in the ice temperature and an increase in the pressure - as the vacuum pump removes the vapor generated. The exact coupling of these three variables namely, jacket temperature --> ice temperature --> and pressure is what I am concerned with.
I know I can determine the pressure if I know the ice temperature (from Antoine's eq.) However the relationship/heat transfer from the jacket to the ice is what I am not sure of?
Do you have an idea of how this equation is set up?