Where would this be
most likely on top of it
can a fan really cool down the compressor
yes, to some extent the more flow the fan has the better... other options (such as immersing the compressor in oil) are usually much more complicated
is there really need to do so?
well you don't need a fan if the total time it is on is 15 minutes... but if you want to use it continuously for 30 minutes or more it will get very hot.. compressors generate a lot of heat and if it not disposed of it can damage the compressor itself
heat does not come from the motor only.. when you compress air it heats up due to compression heating..
the compressor has large mass (heavy casing & oil) and it can absorb quite a lot of heat for the first 15 minutes or so... but after that it becomes a problem
ideally you would like to have fins welded or soldered to the case... as in this example..
http://www.jun-air.dk/graphics/pdf/data ... 3motor.pdf
more area = faster heat disipation