Lasko High Velocity Pro-Performance Pivoting Utility Fan for Cooling, Ventilating, Exhausting and Drying at Home, Job Site and Work Shop, Black Grey U15617 https://www.amazon.com/dp/B077BMBR5B/ref=cm_sw_r_cp_api_i_FH25PTVBW03FTERCDGV3?_encoding=UTF8&psc=1

This is what I have used. Much more powerful than a typical fan.

Thank you, that's very helpful. I take it the window above pops out too? It will be hard to take much advantage of that if so. The trouble with blowing toward these windows is that the air has to take an almost 90deg turn, which will dramatically reduce a fan's effectiveness. I like the concept of an in-line duct blower for this single cooking application, but then you're draping many feet of hose from your kitchen to the window. A blower like this could accomplish that too, though with a 10" orange hose would be much more conspicuous than the hydroponics blowers with 4" or 6" black hoses.

Probably the easiest all-around option would be this blower seated on the window ledge rotated to blow directly out the window opening. The CFM is mediocre, but on par with any twin or triple window fan, though a bit louder. At 14" depth it may not fit entirely on the ledge - possibly one foot could rest on the other side of the lip. You may still need another fan or blower in the kitchen to direct the smoke/smells toward the lower exhaust fan. A similar smaller one maybe?