i too have same doubt..
temperature BC's are very stiff. I would use a convection BC for the fluid imparting the temp to the inner bore - its a little softer - it may or may not be a big deal in this particular case. In certain situations it can be quite significant. Doing both is a good way to see if it matters. Then something like 5 W/mK for hte natural convection coefficient for the exterior should give you a reasonable estimate, assuming the mat properteis and contacts are all sensibly specified.
Only way to know if you are on the right track is to know kind of what the answer should be.
But overall what you're doing sounds ok. Add what bill said and try some other conditions to see if it follows the trends you expect.