B727 ACFT CLBING FROM ARPT AT 800 FT HEARD NOISE AND FELT ACFT VIBRATION ACCOMPANIED BY #2 ENG HIGH EGT AND LOW RPM. THROTTLE WAS REDUCED; VIBRATION DECREASED; BUT CABIN ATTENDANT RPTED NOISE IN CABIN. DEP CTLR ADVISED FLC THAT SMOKE WAS OBSERVED COMING FROM THE ACFT. FLC SHUT DOWN ENG WITH FIRE CHKLIST AND FIRED BOTH FIRE BOTTLES; DUMPED FUEL AND RETURNED FOR LNDG. EXTENDED PATTERN TOOK ACFT OVER CIVIL ARPT WHERE FLC RECEIVED TCASII RA. FIRE TRUCK FOLLOWED ACFT TO GATE.

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NORMAL TKOF UNTIL GEAR RETRACTION; AT THAT TIME FO (PF) INDICATED RUDDER PEDAL MOVEMENT; CREW FELT ACFT VIBRATION ALSO HEARD ODD NOISE. PLT'S INITIAL SENSATION WAS NOSEGEAR/STEERING/RETRACTION PROB; AT GEAR UP FE SAID #2 ENG; I NOTED HIGH EGT AND LOW RPMS AND IMMEDIATELY PULLED #2 THROTTLE BACK ABOUT 2/3. #2 THROTTLE VIBRATION; SMOOTH CLB; FLT ATTENDANT #2 CALLED INDICATING STRANGE NOISE AFT. AT 800 FT NOW; KEPT PWR AT STANDARD; LEVELED OFF STARTED CLEAN UP; ACCELERATION; ADVISED TWR OF ENG FAILURE AND LIKE TO CLB STRAIGHT TO 2000-3000 FT AND RETURN TO LAND. WHEN CLEAN STARTED ENG OUT CHKLIST; DEP ADVISED OF SMOKE; DISCONTINUED ENG OUT AND STARTED ENG FIRE CHKLIST. NO FIRE LIGHT; COOL EGT; PULLED FIRE HANDLE AND DISCHARGED ANYWAY. DIRECTED FE TO DUMP TO MAX LNDG WT. AT 3000 FT TURNED R FOR DOWNWIND. TOLD FLT ATTENDANTS AND PAX SIT AND WILL BE LNDG IN 10 MINS. DEP SAID (BECAUSE OF POSSIBLE FIRE) WE COULD LAND S; I SAID NO BECAUSE OF MAX WT; TAILWIND; ONLY 2 REVERSERS AND NEEDED TIME. STARTED 2 ENG APCH CHKLIST OVER CIVIL ARPT; APCH CALLED TFC GOT TA THEN RED RA; CLB; CLB; TOLD FO TO CLB; AT 3300 FT; CLR TFC. DUMPING; COMPLETED 2 ENG LIST; STARTED LNDG CHKLIST; PREPARE FOR LNDG TO FLT ATTENDANTS. TWR SAID SMOKE SEEN AGAIN; SHOT #2 DISCHARGE. ASKED FOR LONG RWY 35C; RWY 35L CLOSED (OUR FOD AND GRASS FIRE); SECURED DUMP; COMPLETED CHKLIST; NICE VISUAL APCH AND LNDG BELOW MAX LNDG WT BY FO CLRING RWY ASKED TWR IF THEY COULD SEE ANY SMOKE OR FIRE; THEY SAID NO; WE ASKED TO DIRECTLY TO GATE AND I ASKED THEM TO PLACE A FIRE TRUCK RIGHT ON OUR TAIL; THEY DID.