What was found
THE NR 3 ENGINE FIRE WARNING LIGHT CAME ON DURING CLIMB-OUT OF IAH. THE ENGINE POWER WAS REDUCED AND THE LIGHT EXTINGUISHED. WHEN POWER WAS ADVANCED THE WARNING LIGHT CAME ON AGAIN. THE NR 3 ENGINE WAS SHUTDOWN AND THE AIRCRAFT WAS RETURNED TO IAH WHERE IT LANDED WITHOUT INCIDENT. MAINTENANCE FOUND THE NR 3 ENGINE NOSE COWL ANTI-ICE DUCTING BROKEN. THE BROKEN DUCT WAS REMOVED AND REPLACED. LEAK CHECKS WERE GOOD.