THE FLC OF A WDB EXPERIENCED A #1 ENG FIRE ON LNDG ROLLOUT; WITHOUT AN ENG FIRE WARNING.

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FO LNDG SFO RWY 28R. NORMAL APCH AND LNDG. NORMAL REVERSE BY FO. FO DESELECTED REVERSE APCHING 80 KTS GND SPD. AT 60 KTS THE CAPT TOOK CTL OF THE ACFT WITH A PLANNED TURNOFF AT TXWY K. FO STATED 'YOU HAVE THE ACFT; ENGS IN IDLE REVERSE.' CAPT PUT REVERSE LEVERS DOWN AND SLOWED THE ACFT DOWN TO TAXI SPD FOR A L TURN OFF THE RWY ONTO TXWY K. JUST AS THE ACFT CLRED BOTH ACTIVE RWYS (28R AND 28L) HEADING FOR TXWY A; THE TWR ADVISED THAT OUR #1 ENG WAS ON FIRE. AT THE SAME MOMENT FSS CALLED WITH THE SAME MESSAGE. THERE WAS NO COCKPIT INDICATION OF A FIRE. CAPT IMMEDIATELY STOPPED THE ACFT AND COMPLETED THE IMMEDIATE ACTION ITEMS OF THE ENG FIRE CHKLIST. CAPT ASKED FO TO CALL FOR EMER EQUIP AND TO ASK THE CTL TWR TO ASSESS THE FIRE STATUS. TWR REPLIED THAT THE FIRE APPEARED TO BE OUT. CAPT THEN MADE A PA ANNOUNCEMENT ADVISING THE PAX AND FSS AS TO THE ACFT STATUS AND TO REMAIN SEATED. AN ALERT MAINT PERSON WORKING AT GATE X SAW OUR SIT AND CAME TO OUR ASSISTANCE; HOOKED INTO INTERPHONE; SAID HE SAW SOME SMOKE. CAPT THEN FIRED FIRE BOTTLE #2 AS THE EMER EQUIP ARRIVED. SHORTLY THEREAFTER THEY STATED THE FIRE WAS OUT FOR SURE. CAPT AGAIN REASSURED THE PAX ALL WAS WELL AND WE WOULD BE UNDER TAXI SHORTLY. MAINT CLRED THE AREA; THEN GAVE US A SALUTE AND RELEASE FROM GUIDANCE. SO COMPLETED ENG FIRE REF ACTIONS. AGAIN THE CAPT REASSURED THE PAX AND REMINDED THEM OF THE 'SEAT BELT SIGN ON.' WITH TAXI CLRNC THE ACFT PROCEEDED TO GATE AND WAS SECURED IN THE NORMAL MANNER. UPON LEAVING THE ACFT; MAINT WAS BRIEFED BY THE CAPT AND SO. DISPATCH WAS BRIEFED BY THE CAPT AND A CAPT'S RPT WAS SUBMITTED TO THE COMPANY. DURING ALL OF THIS THE ONLY ABNORMAL COCKPIT INDICATION WAS A HIGH EGT READING ON #1 ENG. AS CAPT; THE THOUGHT OF CONDUCTING A PAX EVAC CAME TO MIND IMMEDIATELY. USING ALL RESOURCES AVAILABLE TO ME AND THE EXCELLENT FEEDBACK I GOT FROM VERY PROFESSIONAL AND CAPABLE PEOPLE I REALIZED AN EVAC WAS NOT ONLY NOT NECESSARY IT WOULD HAVE BEEN A VERY POOR CHOICE INDEED. 'CLR' DOES WORK IF THOSE IN COMMAND KNOW THEIR RESOURCES AND HOW TO GET THE BEST FROM THEM. CALLBACK CONVERSATION WITH RPTR FROM ACN #321366 REVEALED THE FOLLOWING INFO: THE FO RPTR STATED THE FIRE WARNING DID NOT OCCUR BECAUSE THE FIRE HAD NO WAY TO GET TO THE FIRE WARNING LOOPS. THE FIRE OCCURRED FROM COMPRESSOR STALLS AS THE #1 ENG CAME OUT OF REVERSE. APPARENTLY THE FUEL CTL WAS SUPPLYING EXCESS FUEL TO THE STALLED ENG AND THE FIRE WAS COMING FROM THE EXHAUST. THE FLT WAS ACTUALLY A FEW MINS AHEAD OF SCHEDULE WHEN IT GOT TO THE GATE AND EVERYONE MADE THEIR CONNECTIONS. AS A RESULT OF THE COORD OF EVERYONE; THE TWR; THE FLT ATTENDANTS; AND THE GND CREW; THE EXPERIENCE WAS A NONEVENT AND NO ONE WAS HURT.