mapj1: 
 

I assume your vacuum vessel is mirror lined so no radiation loss ?.

 

 

And do we ignore conduction heat losses to the outside world via the supply cables?

Z.

Very well said Mike and particularly Chris, I think that you are about right. This reinforces the long piece I wrote above, the time component of overload is very important, and usually not even realised to be there. 

Thanks for all your contributions chaps. I'm going to have to re-read some of these a few times. I'm particularly loving the disparity between what I would consider a fag packet computation and yours though! ? But then I'm one of those who, at least historically, has followed the numbers because I do err in favour of an easy life. Food for though though and clearly some new sums to learn… 

And do we ignore conduction heat losses to the outside world via the supply cables?

Well the electricity has to join or leave at the ends of the test section of cable, depending how resistively that is done heat may flow in or out. But let us concern ourselves with the cable in the middle, and note that in these Gedankenversuchen  (*) we can simply imagine making  the experiment longer & longer until the end effects are far from the section of interest and so become safe to ignore.

In a real experiment, necessarily short, we would instead externally heat or cool the wire ends near the terminations to set a temperature at the ends close to the measured centre temperature, so there was no great lengthways thermal gradient to drive heat either way in that direction. In the language of the maths dept. we would impose a boundary condition of no significant longitudinal  heat flow. Its a lot cheaper than asking site facilities to provide an infinitely long thin lab bench and vacuum vessel ?

Mike

 * something like an experiment in the mind only, literally "thought-experiement"

Have a look at Section 10.14 and Table 10.6 of the IET Code of Practice for In-Service Inspection and Testing of Electrical Equipment.

A 13 A or 10 A fuse may be fitted for appliances rated at 10 A, with 0.75 sq mm flex up to 2 m in length. Someone else has already done the sums to demonstrate this is probably going to be OK, including for fault current protection. BS 7671 permits the non-adiabatic approach in BS 7454 for fault current protection as well (but don't forget there may well be a requirement for protection against overload current).

I would be much more worried about installation conditions than exact fuse ratings

I recently saw an extension reel in a very sorry condition because someone had run it fairly near full load without unreeling it first. A couple of hours and the whole thing had sagged with the cables in the middle fused into each other