RADIATION AND COMBUSTION PHENOMENA PROF. SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA ROOM: Building N7-2 #3304 TELEPHONE : 3714 Cellphone : 010 – 5302 - 5934 swbaek@kaist.ac.kr http://procom.kaist.ac.kr TA : Jonghan Won ROOM: Building N7-2 # 3315 TELEPHONE : 3754 Cellphone : 010 - 4705 - 4349 won1402@kaist.ac.kr

RADIATIVE HEAT TRANSFER RADIATIVE BOUNDARIES FOR ANY OPTICAL THICKNESS RECALL ··· (1) AND AND CONSIDER WHICH MAY BE REARRANGED AS ··· (2) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

Flow Regime *From G.A. Bird

RADIATIVE HEAT TRANSFER CONSIDER THE RADIATIVE ENERGY BALANCE ON THE WALL FROM THE GAS SIDE ! SOLVE FROM 1 & 2 ··· (3) ··· (4) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (1) ALSO, FOR OPAQUE SURFACES ··· (5) ··· (6) ELIMINATE BETWEEN (1) & (5) ··· (7) ELIMINATE BETWEEN (1) & (6) ··· (8) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (3) ··· (4) THEN ··· (7) ··· (8) EQUATE (3) TO (7) AND (4) TO (8) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER NOTE AND THEN ··· (9) ··· (10) IN THE ABSENCE OF CONDUCTION, THERE EXISTS A “TEMPERATURE JUMP” ON BOUNDARIES, AND PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER FOR MIRROR BOUNDARIES (PERFECTLY REFLECTING BOUNDARIES) ··· (11) HOME WORK SHOW FOR (T,J) FORMULATION THAT, IN TERMS OF J, ··· (12) ··· (13) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER FOR MIRROR BOUNDARIES ··· (14) EXAMPLE STEADY PURE RADIATION (RADIATIVE EQUILIBRIUM) BETWEEN TWO VERTICAL PLATES PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER FROM RADIATIVE ENERGY THEN RADIATIVE MOMENTUM BECOMES ④ OR PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (9) ··· (10) INTEGRATE OVER ··· (15) FROM (9) AND (10), IN VIEW OF SUBTRACT ··· (16) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER REARRANGE (15) WITH (16) WHICH GIVES PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER EXAMPLE THERMAL BALANCE RAIDATIVE BALANCE ··· (1) ··· (2) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (1) USE, LINEARIZE ··· (3) INTRODUCE , , BOLTZMANN NUMBER ELIMINATE dT/dx BETWEEN (1) AND (3) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER LET ONLY NEGATIVE ROOT IS PHYSICALLY MEANINGFUL ! ··· (4) WALL BOUNDARY CONDITION PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (4) INTRODUCE ,LINEARIZE AND NONDIMENSIONALIZE ··· (5) INSERT (4) INTO (5) WHICH GIVES PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (1) THEN ··· (6) FROM (1), THERMAL ENERGY ··· (7) AS , , ··· (8) FROM (7) AND (8) ··· (9) OR PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER (6) (9) INSERT (6) INTO (9) ··· (10) FOR THE TEMPERATURE JUMP, LET ··· (11) REARRANGE PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER

RADIATIVE HEAT TRANSFER ··· (10) INVERT FOR DIMENSIONLESS JUMP ··· (12) IN TERMS OF (12) , REARRANGE (10) PROPULSION AND COMBUSTION LABORATORY RADIATIVE HEAT TRANSFER