Heat Loss Through Stagnant Branch

[ChemEng2010]

We have been asked to investigate potential ice/hydrate problems in a non-flowing branch off a normally flowing line. Worst case ambient conditions is -9°C and the main line normal operates at ~50°C. The branch is only a couple meters long but ideally I'm looking for a temperature profile per unit length to prove that we are more than adequately covered. Any suggestions on how to progress this. Most heat transfer equations involve steady-state and with a mass flow, which is not valid in this case. Any advice would be welcomed!

 

[hacksaw]

it is a conduction problem if you want to calculate, the best bet is to heat trace the line as part of the freeze protection