No, opening the door of a refrigerator in a closed room will not cool down the room faster than keeping it closed and running only a fan inside the room. In fact, opening the refrigerator door in a closed room can have the opposite effect.
When you open the refrigerator door, the cold air inside the refrigerator escapes into the room, while warmer air from the room enters the refrigerator. This exchange of air leads to an increase in the room's temperature rather than cooling it down. Additionally, the refrigerator's compressor will need to work harder to cool down the warmer air that entered, which can result in increased energy consumption.
On the other hand, running a fan in a closed room without opening the refrigerator door can help circulate the air and create a cooling effect through evaporation. As the fan blows air across your skin, it enhances the evaporation of moisture from your body, providing a sensation of cooling. However, it doesn't actually reduce the overall temperature of the room.
To effectively cool down a room, it is better to use an air conditioner or a dedicated cooling system designed for that purpose. Air conditioners are specifically designed to extract heat from the room and lower its temperature.