In a hot, closed room with just one opening (say, the door), where should a moveable fan be aimed for maximum cooling of the room. What is the science behind it?
For example since hot air rises...if the fan is on the floor it should be aimed towards you? And a higher elevated fan aimed outside the door to blow the hot air out?
ETA: Cooling the room. I assume to cool self you turn fan towards self...
This depends on your environment. If the temperature is cooler outside the room blow the air into the room with the fan either in the doorway or just outside it to get the cooler air into the room. If the room is cooler than outside close the door. If they are the same temperature it won't matter. I've found that blowing cooler air up and at angles to the walls helps keep the whole room cooler since it circulates throughout the room and helps keep the hot air at the ceiling from getting really hot.
Since there is only a single opening, air would have to flow both in and out of the same passage. To direct the coldest air into the room, place the fan at bottom.
The fan should be well outside the door, facing towards the door. Imagine if you could see the air coming out of the fan, that it's bright green. It gets wider and spreads out as you get further from the fan. You want the fan far enough away that the entire door is taking up by the bright green air.
Searching for how firefighters ventilate a room will give some good pictures 
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What is the science behind it?
Both airflow directions will be able to exchange the same volume of air. The fan will not produce a vaccuum, because there will be a flow in the opposite direction. This opposed air flow will be more turbulent. Keep simple physics in mind:
To answer the question: Just maximize the air flow, by not blocking it. The direction will not influence the volume of exchanged air. However try to blow the warm air at the top of the room out.
To improve the usage of a ventilator
Most benefitial for cooling is evaporation. This physics effect is based on needed energy to overcome "latent heat". Just remeber the chill when rising out of a lake after swimming at windy weather. The water droplets on your skin have the temperature of the sea. Then they evaporate and cool your skin. A bowl of water before the fan will not help much. However just wetten your skin - maybe use a wet towel or blanket during sleep.
In addition to optimizing the air flow of the ventilator, there are amazing tricks for hot summer nights:
The basic statement you must keep in mind is that a fan does not cool. It just moves some air, slightly warming it (the motor heats while working).
The fan will "cool the room" ONLY IF the air on the other side of the opening is already cooler. Otherwise, your endeavor is useless (or even damaging, if the incoming air is actually hotter).
If you want to cool yourself, then aim the cooler directly to yourself. That will help the evaporation of your perspiration, temporarily and locally cooling your body.
Place the "FLOOR" fan (which is what most people have) in the doorway and angled upwards. This pulls the lowest/coolest air from area outside the room, as well as blowing it upwards into the room to mix with the highest/warmest air. The cooled air up top will tend to fall lower and be replaced by the remaining somewhat warmer air in the room until it reaches a temperature equilibrium. Since you can't outright displace the air in the room with the air outside the room (as in ALL the air outside the room displacing ALL the air as it enters the room), this way is most efficient as it ensures maximum circulation. As for the science behind it: warm air rises over cool air (as it partially warms it), and cool air settles under the warm air (as it partially cools it). *If you aim the fan low, you will cool the lowest air most, but cool the upper warmer air least.
