A clothes dryer can produce a whining noise for any number of reasons. If the noise occurs each time you run a dry cycle, then it's probably time to investigate its cause. Since most noises occur when a component malfunctions or is starting to fail, it's generally best to get your dryer inspected by a dryer repair specialist who can identify the problem and replace the faulty part.
Gliders are the plastic or nylon seals that surround the rim of the drum. They protect the drum from rubbing against the metal cabinet when it turns. Over time gliders can wear, and as they diminish you can sometimes hear a whining sound when the dryer is running. Switch out the dryer's worn gliders with new ones. Since they usually come as a set, replace them all at one time.
Rollers are small metal wheels located on the drum's exterior to help it turn in the cabinet. They can become damaged from continued dryer use. When even one of the rollers begins to deteriorate, it's likely to create a squeal or whining sound, as the drum tumbles clothes. Change out bad rollers for new ones. Like gliders, rollers come as a pair. Replace them all at once, so the parts wear consistently.
Drum Belt Slips
Around the centre of the drum is a rubber drum belt. It stabilises and supports the drum, so it can rotate in a uniform circle to dry clothes evenly. If the belt slips from its position, you will likely hear two distinct sounds: thumping and whining. The thumping will occur if the belt's slippage causes the dryer to spin out of control so that it knocks the sides of the cabinet. The whining sound will be made by a loose belt that struggles to maintain its position on the drum despite little to no tension. Consult your dryer manual for instructions on how to find the belt. If you locate it, and it's no longer around the drum's centre, have it replaced. You can't reposition a loose belt.
Broken Idler Pulley Wheel
If your dryer's idler pulley is faulty, its wheel will whine and screech as it tries to turn. The idler pulley is a mechanism that keeps tension on the drum belt, so it stays in place while it moves the drum. Without the added tension from the idler pulley, the belt would come loose from the drum and the drum wouldn't spin evenly. It's a three-part component that consists of a wheel, bracket and spring. The belt loops over the bracket, under the motor, and circles the drum. Review your dryer manual for help locating the component on your model. It's usually near the front of the dryer below the drum. Try to manually operate the wheel. If it moves slowly and you experience any resistance, replace it. Swapping out the faulty part should quiet your dryer.