First of all the total width of your case is 191mm, so this is not the available space you have height wise for a cooler, the best thing you can do is get a tape measure and measure the distance from the top of your CPU to your cases side, i very much doubt the nhd14 will at all fit in your case and to be honest i do not think you would be well served with one in the elite310, as for a cpu cooler to work well it needs a good supply of cool air, you would be much better served by buying a new case and a new cooler such as a Coolermaster HAF 912 case together with a CoolerMaster Hyper 212plus CPU cooler, both of these can be had for only a little extra cost of what the nhd14 would cost...
Coolermaster HAF 912 Plus, Black Chassis = £61
Coolermaster Hyper 212 Plus CPU Cooler = £22
Total Cost = £83
As opposed to a...
Noctua NH-D14 Dual Radiator and Fan Quiet CPU Cooler