To save space, I am hoping to stack my washer/dryer, but to reach the knobs on the dryer, I'm wanting to turn the dryer on its side. I cannot see any reason this would not work, provided I've built a good stand, etc. Is there any mechanical reason a dryer would not work properly on its side?

Thanks!

The circulation of hot air is calculated for an upright position.
By placing it any other way there may be serious problems with the heat distribution inside the tub and the rear , where the motor , wiring , and other parts are located.
You should at least contact the service department of the manufacturer of the dryer to discuss this intention, and hear their suggestions.

Succes !