1st try turning every pulley and ancillary ( power steering pump , alternator etc) by hand. All should turn easily (with the exception of the AC pump) with no grittyness or wobbly pulleys- If you do find a sticky pump / alternator then it should be replaced or repaired
If the engine is stone cold you can briefly run it with no belts to see if the noise changes or has gone away, this will help show if an ancillary is the issue
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ok so is the whine there with the belt removed and running a stone cold engine?
if its still there then it could be a vacuum leak on the inlet as these can also produce a whistle or whine
The best way to locate a leak is to have the engine running and warm and then spray lighter gas /propane around each joint in turn. If the engine rev's up you've found your leak.
Now you might think that spraying lighter gas around a hot engine isn’t wise, however the flash /ignition point of gas is about 400°C so you need a naked flame or spark to set it off and I’ve used this method for many years without incident.
Work your way through each possible joint one at a time and you should find it. I use a slightly flattened piece of brake pipe and some rubber hose from the can of lighter gas to provide a spraying 'wand' and allow a direct blast of gas into each area, especially those difficult to reach with large implements.
Ok thanks for the extra info
so if the noise only starts once things are warm then its possibly a vacuum leak as they are strongly effected by engine and ambient temperature as inlet system parts expand and can then move away from each other
please check it out and let me know what you find