When cooling a room with a box fan, placing it on the floor is generally more effective than putting it high on a shelf. This is because of the way air circulates and how fans work.
Heat rises, so the air near the ceiling of a room tends to be warmer than the air at the floor level. When you place a fan on the floor, it can help create better air circulation by drawing in the cooler air from the lower parts of the room and directing it upwards towards the warmer ceiling area. This process is called convection, and it aids in equalizing the temperature in the room.
Placing the fan on a shelf or high on a wall might not be as effective because it will primarily circulate the air in the upper part of the room without effectively mixing the warm and cool air. It won't have the same cooling effect on the overall room temperature as a fan placed at the floor level.
Additionally, having the fan on the floor can create a wind chill effect, making you feel cooler even though the room temperature remains the same. The air movement across your skin helps with evaporative cooling, which is why you feel cooler when the fan is blowing directly on you.
In summary, for better cooling efficiency and temperature equalization, it's generally more effective to place a box fan on the floor rather than high on a shelf.