What was found
ON T/O, PRIOR TO FLAP RET, A/C DISPLAYED A MOMENTARY LVL 3 ENG 2 A-ICE DUCT ALERT. AS THROTTLE WAS BEING MOVED TO IDLE ALERT WENT AWAY. CLIMB TO FL 290 WAS UNEVENTFUL UNTIL 30 MIN INTO FLT WHEN A/C DISP LVL-1 ENG 2 A-ICE OFF ALERT, WITH A CONS OF ENG 2 A-ICE DUCT HAS FAILED. ENG SHUT DOWN IN FLT (QRH) WAS PERF AND APPROX 50K FUEL WAS DUMPED. INSPECTED ANTI-ICE DUCT FROM NR 2 ENG FIREWALL AFT R/R`D SENSING ELEMENTS D89, D90, D91 IAW MD-11 MM 30-22-11-4. REPLACED BURST DETECTION UNIT PER MD11 MM 30-22-10-4. PERF MAX POWER ASSURANCE ON NR 2 ENG AND RAN FOR APPROX 5 MIN WITH NO FAULTS OR ALERTS. NR 2 NOSE COWL ANTI-ICE OPS CHECK NORMAL PER JRH 4-28. A/C OK FOR SVC.