Is it from the wheel? If so, then it could be numerous of things: worn hub bearings, worn brake pads/shoes/rotor, faulty drive axle...listen carefully and take you car to a certified mechanic!
if its a front wheel drive vehicle then it could be the axels
main shaft bearing
A bad transmission. The sound is from metal grinding on eachother.
could be a wheel bearing...or just that its a french car
A defective vacuum line can cause a whistling sound when the vehicle is accelerating. A loose belt can also create a high pitched whistle sound.
bad wheel bearings
When the wheel and the tire rub together.
Transfer case is shot.
check your wheel bearings.
More than likely... the power steering belt.
What would cause a grinding noise after a tire is replaced and the brakes are not worn?
The grinding sound when accelerating could indicate a worn-out CV joint or a problem with the transmission. The loud whirring noise at all speeds could be due to a failing wheel bearing or an issue with the differential. The higher engine temperature than normal could suggest a problem with the cooling system, such as a failing water pump or a blockage in the radiator.