What is the Optimum Thickness for a Thermal Container Design?

[joaquinjbs]

Hello everyone, first of all, thank you very much for reading.

I have to design a container (100 mm of height and 80 mm of interior radius of XPS) to keep a cryogenic mix (water and salt ice) at -15ºC at least for 40min. And my problem is to calculate the optimum thickness of XPS.

I've been reviewing thermodynamic and heat transfer theory. I have conduction and convection so if I increase the thickness, I improve conduction but it's not good for convection. Also, I don't know how to connect the thermodynamics and heat transfer theory with warming the ice. I'm having some problems with the convection coefficient too.

If somebody could help me I would be very grateful. Thanks!

 

[joaquinjbs]

I tell you what I have do at the time.

With specific heat of the mixture, the mass and the temperature difference between exit refrigerator temperature and -15ºC I calculate the heat.
On the other way, I obtain the heat of convection and conduction with the equivalent resistance (in a cylinder), and finally, I equalize at the previous heat.
I could calculate the exterior radius if it were not for the convection coefficient and the external temperature of the cylinder. And I can't give the time which I want (40min.)

Any idea? Thanks!

*Edit: -15ºC is the melting point of the cryogenic mix, therefore I can add the latent heats of fusion.