Answer
a. The fan should blow downwards.
b. The fan should blow upwards.
Work Step by Step
No matter which way the fan turns, a convection current is set up that mixes the air in the room.
Assume that the people in the room are gathered more near the center.
In the summer, the fan should drive air downward, quickly, to evaporate perspiration and give the occupants a wind chill effect.
In the winter, the fan should slowly pull warm air upward so it is forced out toward and then down the walls, avoiding the wind chill effect.
