I had this problem with my mid-2014 15” mbp. Mine would pretty reliably shut down soon after opening a browser. If I opened nothing, or just copied files, it might go 30 minutes before shutting down. First screen would go black, then it would turn off after about 5 seconds. I reset NVRAM and SMC, no help. I did a clean install of OS X. No help. I had already replaced the topcase/battery on this machine a while back. This machine has seen extremely heavy use for the about 5 years I’ve owned it. So because one of my fans would make a lot of noise under load (had been going on for months) I had already ordered 2 new fans. Was just procrastinating replacing those. So I replaced the old and very dusty fans and at the same time replaced the very old and crumbly thermal paste. Removed all the random dust bunnies from the inside. Put it all back together. Fixed!