Bit of a quandary, my current build based around an AMD A10 7850K with a R480 4Gb is serving me well enough bar one issue which is noise. Mainly it seems from the GPU. I can leave it crunching numbers all day and its still quiet, though 15 minutes of gaming and the graphics card fans spin up loudly. Card is meant to be quiet being the MSI big twin fan unit which is supposed to be quiet. My initial thinking is basically the GPU fans are being starved due to their location, couple of generic images of the case with a graphics card below An this is the case closed, note there is a factory fit dust filter on this too I'm going to remove the filter but I doubt it will do a massive amount, the fans pretty much flush against the case so, get the saw out or something else?
Have looked at the fan profile speeds ? You can set custom profiles if you enable something that maxes the card you can adjust till you get a decent balance You could look at a replacement gpu you can get low profile Nvidia 1070s that run close to silent Scan and Overclockers both have such cards for around £400. This would reduce the noise output
Leaving the case off and running your tests should show if its the dust filter blocking things. Something like MSI Afterburner might allow you to tweak things downward and make it less noisy at load.
Fans right up against grills/intakes/mech is going to make noise (and slightly reduce fan performance), at least ~1cm of standoff distance is a good rule of thumb to avoid that. Without expensive solutions (replace GPU, replace case with fanless case, swap card cooler with AIO cooler), you could try removing the existing card fans and shroud, adding some larger slimline fans (to gain spacing with side of case) and adding a duct to direct the airflow from the larger fans into the heatsink rather than spilling around it (cardboard and tape works as well as fancy 3D printing).
Case off ill try tonight along with MSI after burner see if I can work out anything, I will need to try case on though to get an idea of temps as well. Annoyingly im limited on spacing due to the slot placement on ITX boards so it will always been pinned to the side. The AIO may work, its a little snug in the case so not total ysure how I would route the piping but we can see. I have had a look in there, theres nothing really in there dust wise thankfully. I did try an hunt down a slimline 1070, seems they are less common than rocking horse poop, shame as it would solve the problem totally.
Yeah first stop has to be playing around with the fan profile, takes very little time and no money etc.