What was found
WHILE CLIMBING OUT OF 21,000 FEET, GOT MULTIPLE RT ENGINE FIRE, ANNUNCIATIONS AND A R ENG FIRE EICAS MESSAGES. WERE IN CLEAR AIR. HAD RECENTLY TURNED OFF THE ENGINE ANTI-ICE BECAUSE OF AN ICE INDICATION AS WE CLIMBED OUT & MANEUVERED AROUND THUNDERSTORMS & HEAVY RAIN. WHEN THE INDICATION, WERE IN CLEAR AIR, BUT HAD FLOWN THROUGH SOME HEAVY RAIN. EACH INDICATION LASTED ABOUT 3 TO 5 SECONDS WITH ABOUT 10 SECONDS IN BETWEEN EACH ONE. & THEN THEY JUST STOPPED. REMOVED AND REPLACED RT ENGINE COMBUSTION LOOP DUE TO CHAFING & KINK THROUGH OUTTER CASING. IAW AMM 26-11-10. PERFORMED OPS TEST OF THE ENGINE FIRE/OVER DETECTION SYSTEM IAW AMM 26-11-00. OPS CHECK GOOD.