Question

Why is an air-conditioner normally installed at the height in a room?

Answer 1

The convection currents are the main reason i.e. Warm material that is lighter (less dense) rises, while cooler material that is heavier (more dense) sinks. It means that the warm air of the room rises up and the cooler air sinks.

Complete step by step answer:
Cold air is heavier than warm air.
When an air conditioner is set at a given height, it cools the air around it, and because the cool air is heavier, it flows towards the room's floor, displacing the warm air that was previously there. This warm air is cooled by the air conditioner again, and the cycle repeats. The room will be uniformly cooled as a result of this.
If the air conditioner is located at the bottom of the room, it will chill the air around it, which will remain at the bottom. Because the warm air that rises to the ceiling remains warm for an extended period of time, the cooling is ineffective.
When the temperature rises, the air conditioner cools the air and makes it denser. As the pattern continues, the space will become cooler.
We too keep our heater on the floor for this reason.

Note:
For the maximum cooling performance in a $10$ foot-high room, a split type AC should be positioned at $7$ to $8$ feet. The optimal height for a window air conditioner is $3$ to $4$ feet off the ground. Because heat dissipation is impossible when the AC is mounted near to the wall or in an airtight space, it will trip owing to high head pressure.