Strange clicking noise when fan is on iMac 21"

Hi - I have a late 2013 iMac 21", running a normal hard drive (not solid state). It has always behaved impeccably. Recently, one of my children has started playing a game regularly on it called Roblox. Over the last few weeks, quite often I hear that the fan has come on whilst she is playing the game. The normal fan noise is frequently accompanied by an unusual clicking noise, like a combination of a thin piece of plastic being flicked quickly and the noise you hear when a toilet cistern is dripping after being flushed. The noise is definitely coming from the back of the iMac near the fan. I have twice found that if I ask her to stop playing the game and then tilt the screen up and down and swivel it around, the clicking noise stops temporarily.

The other strange thing is that, so far, this clicking noise has not occurred in the normal operation of the iMac - only when she is playing Roblox. Having said that, Roblox is the only intense game played on this iMac, so if it is something to do with game playing in general, we have no other comparisons.

Having read other posts describing something similar, I am reluctant to go to a service centre and find that they charge me a lot of money to replace something or carry out work, which doesn't fix the problem. There do not appear to be any other problems with this iMac

Has anyone else had the same thing happen and if so, what did you establish was the issue ?

Grateful for your replies