They work, but not sure about the cheapies. Mine is branded EcoFan by Caframo Not sure they move enough air to make much of a difference, though. I’d guess not. I do like mine, however, as I can judge the stovetop temperature by how fast it’s spinning. I might be a bit lazy there, though…
My dad had wondered about them for years, so I bought a cheap one on amazon and had it shipped to him. It works quite well but started rattling after about a year. A family friend eventually gave my parents a more expensive model that is noticeably sturdier and silent. I think they move a good amount of air for what they are. I'd say they're equal to my insert blower on the lowest setting.
I like them! They don't move as much air as an electric fan but they are also silent. I can't stand fan noise so these are a good alternative.
I have one that really just lets me know the stove temperature, the ceiling fan moves the air much more efficiently
We have 2 on top of our cabin stove. They work fine, pushing heat over and under the loft area (without the pot in the way... lol). Look closely at this pic, as to where the fan is placed. It's important. In that location, on that stove, it draws cool air thru the top fins, from behind the stove, while sitting on the hottest top surface. That difference in temps is how the fan generates heat. The more difference, the faster the fan turns. Some stoves have top areas that won't allow a fan to sit there, or the top surface isn't the hottest area. An Eco fan will still work, but not very well on those stoves.