Lexus es 330 engine whirring noise?

I have a 2006 lexus es 330 that just turned over 90,000 miles. My dad and I have done the regular maintenance on it so far but this weekend after a 3 hour drive, I turned the car back on and a loud whirring/humming/whining noise was coming from the engine. It get’s slightly louder with acceleration, but I can barely hear it once I’ve picked up speed (but it’s still there.) It still happens when I am in neutral. It sounds like it is coming from the passenger side of the engine. Close to the power steering pump area, but the power steering fluid is full (although it is a very dark/black color and has a slight smell…not sure if this is normal.) I’m not having any trouble or hesitation while steering. The rack is operating smoothly and it is not leaking. I plan on taking it into the shop but wanted to go in educated. Any ideas?

Anything with a pulley is suspect. And the timing chain. A stretched timing chain can whirr along with the engine’s RPMs. While your miles accumulated seems too early for a timing chain stretch, the miles vs. years suggests lots of around town driving, and this can make a dramatic difference. 90,000 around town miles is easily worth 180,000 highway miles.

Thanks for the reply. I took it into the shop and they suspect it is the alternator. Hopefully the replace will fix the problem.

Thanks for the follow up post.
Sincere best.