Hi,

I own a 500 1.3 Diesel Sport (2010 model), 40,000 with full service history.

Unfortunately it makes a high pitch whining noise, usually when revved between 2000 -3000 and continues once the engine is switched off for 5-10 seconds. From reading forum posts i think it is an electrical (solenoid) issue related to the Throttle Body. - I've had the air box off and filmed the issue which i will upload shortly to Youtube. My local fiat garage say its normal, but i am not convinced! Any thoughts on this issue would be most appreciated.
Thanks

Diesel's don't have a throttle body.
I assume it will be a common rail diesel, in which there is 1 fuel line at very high pressure feeding the electronically controlled injectors. The high pressure fuel line can run at up to 23-24000 psi.
Are you sure the whine isn't the turbo spool ? Is it a turbo diesel ?
This would make sense with the whine still being apparent after switch off.
Really you should let the engine idle for a minute or two before switching off the engine to let the turbo "spool down", if the turbo is still spooling fast when the engine is switched off you will starve it of lubricating oil. This will lead to oil seal failure and can result in "diesel run away" which results in engine self destruction.
Don't forget diesel engines will happily run on their own engine oil ( which is what lubricates the turbo), and they will "run away" until all the oil has gone. Which is when the engine self destructs rather spectacularly.

Thanks John, the noise also comes on after 5-10 seconds if the key is turned in the ignition, but not far enough to start engine, hence thinking it was an electrical issue. Interestingly, the pitch is always the same, constant and switches on/off in an instant.

I've uploaded the clip to youtube.com/watch?v=DygSlsWXbVY

Definitely not turbo, is that the inlet manifold at the back of the engine ?
I haven't had a look at the 500 diesel.
The little black box that you end up near at the end of the video, is that by any chance on top of the EGR valve ( Exhaust Gas Recirculation) ?
If it is it looks as though the EGR valve is electronically controlled, the valve itself could be clogged up with carbon. The whine will be the controller trying to operate the valve.
If the electronic EGR is similar to what's on the 2.2D X Types then the only solution is a new EGR valve. Euro 4 and earlier valves could be cleaned and blanked like what is on the 2.0D X Type.
Does the car hesitate and stutter under light load when cruising ? The trigger speed on the X Type was 50-55mph. Its when the valve is opening and closing.
Best bet would be to remove the valve and inlet manifold and having a look inside, if its all coked up then you have something to start at.