Samir,

To explain a little better.  This is actually a piece of a much larger problem, but due to the type of problem, there are a number of symmetries that can be used to 'simplify' the problem.

What I am trying to model is a subsea pipeline that is initially flowing, with the assumption that the internal liquid is at a constant temperature across the cross section of the liquid.  At Time Zero, the flow in the pipe stops and is allowed to cool through conduction to the ambient temperature.

This is made a little bit more complex by the fact that when the pipes are joined together, the section that is welded together has to be insulated with a different insulation.  I want to find the location of the pipe that reaches a certain temperature first and how that develops over time.

I hope this helps.

Best regards

Andrew Lindsay