What was found
DURING CLIMB OUT ON FLIGHT 3441 FROM LGA TO IND, "RUD HDOV PROT FAIL", "BLD VLV 2 FAIL", AND "BLEED 2 VLV CLOSED" MESSAGES APPEARED ON EICAS. WITHIN TEN SECONDS THE NR 2 ENGINE SHUTDOWN AND "ENG 2 OUT" MESSAGE APPEARED ON EICAS. THE CREW ATTEMPTED AN APU ASSISTED AIR RESTART, BUT THE ENGINE HUNG AT 36.5%. AN EMERGENCY WAS DECLARED AND THE CREW RETURNED TO LGA. MAINTENANCE INSPECTED THE ENGINE AND FOUND NO VISUAL DAMAGE TO THE INLET, FAN, OR EXHAUST AREAS. FADEC'S 2A AND 2B WERE REMOVED AND REPLACED. UPON FURTHER INSPECTION, MAINTENANCE FOUND THE YELLOW FACEC HARNESS CHAFFED AT THE CONNECTION TO THE PYLON. REMOVED AND REPLACED E2 YELLOW FADEC HARNESS AND PMA ASSEMBLY. OPS CHECK GOOD.