usfence -
I don't fully picture the situation that you have, so some of this may reflect errors in my understanding.
If I understand correctly:
3 hollow cross section of PVC, hot
3 streams of very cold (-140F) nitrogen gas put inside at 100 mi/h
metal die both internal and external
To analyze the system I would look at the heat transfer between:
outer die and air, both convective and radiative
outer die and any heat source, including the hot PVC (contact, I assume)
inner die/mandrels and PVC and/or N2
hot PVC and N2 (I assume the N2 is flowing with the PVC not across or against the flow)
The heat transfer analysis would require information about the heat transfer coefficients for each of the stages listed, mass and thermal property information, flowrate information. The flowrate information is vital to establishing the heat balance limits, i.e., temperature rise of matl A vs corresponding T drop of matl B - such as N2 and PVC.
The geometry will come into play. The heat transfer by conduction through each material will come into play.
For first level answers, a lot can be simplified and ignored. You could for example, compare the heat "supplied" by the flow of PVC to the possible heat removed by the N2. This would be straight heat balance, not heat transfer. It will establish the possible limits, that would be approached to some degree as limited by the heat transfer and contact time or distance.
If the geometry cannot be ignored, then you need to develop a model of the system. My approach, which is one of the services I offer, would be to build an FEA model of the system and develop the combination of heat balance and heat transfer information for all the parts of interest.
HTH, let me know if I can be of assistance. You can find me through my website.
Jack M. Kleinfeld, P.E. Kleinfeld Technical Services, Inc.
Infrared Thermography, Finite Element Analysis, Process Engineering