'03 Santa Fe- I need help, high pitched engine whine after > 20 miles of driving

I have an '03 Santa Fe, which I've had little trouble with until
recently. I have about 25K miles on the vehicle. This summer we had
the oil changed at a local super lube place. Shortly after that I was
driving on a warm day with A/C on (and the recirc. button on), when I
started to hear a high pitched engine whine when I rounded corners or
when I put my foot to the accelarator. The temp gauge was reading like
normal and no dash lights came on. When I got home I looked under the
hood and power steering fluid was bubbling out from under the cap. I
took it to the dealer, they said the super lube place must have over
filled the reservoir. Should be fine. Well it wasn't. When I drive
continuously for greater than 20 mins I get the high pitched engine
whine. I took it back and they replaced the power steering pump. The
day we got it back, same problem with the fluid coming out from under
the power steering resevoir cap. When it cooled my husband removed
fluid to between the min and max lines. Now the fluid doesn't bubble
out but I still get the whine. Recently I drove about 50 miles to a
nearby city. I don't recall having trouble getting there in the
morning. On the way home, I was again running the A/C and had trouble
with the sound again. It was much worse this time as my uninterrupted
trip was longer. If I do stop and go driving, I don't get the whine.
The noise doesn't sound like a fan noise, it is much louder and
distint.
I want to take it back to my dealer, but I'd like to know what to tell
the dealer to look for. They won't be able to reproduce the noise if
the car isn't driven for over 20 miles. I don't know if the A/C use is
even a factor in whether or not it happens.
Please help send the dealer in the right direction!

The only other engine issue I've had was that it recently died at a
stop sign after I applied the brakes to stop. It started up again
without trouble. No other issues like this again.

Thanks in advance for any help you can give,
Christi

 

Just tell them what it's doing and how to make it happen. It doesn't
really matter very much what you tell them to look for. They're going to
look for whatever could cause the condition you describe.