We say "turn the volume of the TV up/down".
Do we say "turn the strength of the fan up/down" as the fan has a few buttons for you to adjust the strength of the air blow?
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to increase the amount of sound, heat, or light produced by a piece of equipment by pressing a button or moving a switch
"The amount of airflow" isn't on the list, but it's a rather natural extension of that definition. You can either turn the strength of the fan up, or, more naturally, just turn the fan up.