You would want to use a blower style GTX 970 (blower style GPUs blow fan hot air out the case, while the others move air into the case). PNY and EVGA have GTX 970s that should fit in the X51. ASUS, Gigabyte and I think Gainward does as well, but ASUS and Gigabyte's are overclocked, so they aren't generally recommended.
Currently owned computers:
AW13 R2 | i7-6500U | GTX 960m 4 GB + GA (R9 285 2 GB / RX 480 8 GB) | 16 GB 1600 MHz | 1800p Touchscreen | 2 x 500 GB SATA M.2 | Graphics Amplifier Performance Analysis with 13 R1
Desktop | i7-3770 | GTX 980 4 GB | 16 GB 1600 MHz | 120 GB mSATA + 960 GB SSD + 2 TB HDD | 600w PSU
Formerly owned computers:
HP Pavilion 15-n280us (given away) | Apple Mac Mini 2012 (sold) | m15x (damaged mobo) | 13 R1 (death by unknown) | m14xR2 (Tradied In)