1. RADIATION AND COMBUSTION PHENOMENA
PROF. SEUNG WOOK BAEK
DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA
ROOM: Building N7-2 #3304
TELEPHONE : 3714
Cellphone : 010 –
TA : Jonghan Won
ROOM: Building N7-2 # 3315
TELEPHONE : 3754
Cellphone :

2. RADIATIVE HEAT TRANSFER
GAS RADIATION
IMPORTANT DISTINCTION
A CRUDE ANALOGY
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

3. RADIATIVE HEAT TRANSFER
GAS RADIATION
THIN GAS,
THIS SOLUTION IS OBTAINED FROM THE INTEGRATION OF
ITS COMPARISON TO
REVEALS THAT FOR THIN GAS
ONLY ENERGY EMISSION WITHIN THE MEDIUM IS CONSIDERED. EMISSION APPROXIMATION (S&H, P745)
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

4. RADIATIVE HEAT TRANSFER
GAS RADIATION
THEN, THE RADIATIVE CONSTITUTION
IS REDUCED TO
INTRODUCE THE PLANCK MEAN ABSORPTION COEFFICIENT
WHICH, HOWEVER, CAN BE APPLIED FOR THE EMISSION TERM IN A GAS OF ANY OPTICAL THICKNESS (S&H, P.745)
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

5. RADIATIVE HEAT TRANSFER
GAS RADIATION
THEN OR
CONSTITUTION EQ FOR THIN GAS RADIATION
ACCORDINGLY, THE RADIATION AFFECTED THERMOMECHANICS OF THIN GAS ARE
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

6. RADIATIVE HEAT TRANSFER
GAS RADIATION
WHICH GIVES
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

7. RADIATIVE HEAT TRANSFER
GAS RADIATION
THICK GAS,
ASSUME CONSTANT
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

8. RADIATIVE HEAT TRANSFER
GAS RADIATION
NOTE
CONSIDER TAYLOR EXPANSION
TRUNCATION OF THE SERIES AFTER A FEW TERMS WILL GIVE AN ADEQUATE REPRESENTATION OF THE
AT NEAR
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

9. RADIATIVE HEAT TRANSFER
GAS RADIATION
THEN, INTENSITY BECOMES OR OR
FOR (OR )
, FOR THICK GAS
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

10. RADIATIVE HEAT TRANSFER
GAS RADIATION
FOR THICK GAS, A LOCAL INTENSITY DEPENDS ONLY ON THE MAGNITUDE AND GRADIENT OF THE LOCAL BLACKBODY INTENSITY (S&H, P.751)
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

11. RADIATIVE HEAT TRANSFER
GAS RADIATION
HEAT FLUX FOR THICK GAS: DIFFUSION APPROXIMATION
REARRANGE OR
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

12. RADIATIVE HEAT TRANSFER
GAS RADIATION OR
IN TERMS OF THE ROSSELAND MEAN
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

13. RADIATIVE HEAT TRANSFER
GAS RADIATION
HEAT FLUX BECOMES OR
CONSTITUTION EQ FOR THICK GAS RADIATION
ACCORDINGLY, THE RADIATION AFFECTED THERMOMECHANICS OF THICK GAS ARE OR
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

14. RADIATIVE HEAT TRANSFER
GAS RADIATION
WHICH GIVES
HW#4 [REF.1] P.593 #12-1~4
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

15. HW#4 [REF.1] P.593 #12-1~4
12-1. A spectral beam of radiation at and with intensity enters
a gas layer 20 cm thick. The gas is at 1000K and has an absorption coefficient
. What is the intensity of the beam emerging from the gas layer? Neglect
scattering, but include emission from the gas.
12-2. Radiation from a blackbody source at 3000K is passing through a layer of air at 12,000K
and 1 atm. Considering only the transmitted radiation (that is, not accounting for emission
by the air), what path length is required to attenuate by 25% the energy at the wavelength
corresponding to the peak of the blackbody radiation?
12-3. Radiation with a wavelength of is passing through a gas at a temperature of
10,000K. What is the ratio of the true absorption coefficient to the absorption coefficient?
12-4. A gas layer at constant pressure P has a linearly decreasing temperature across the layer
and a constant mass absorption coefficient (no scattering).
For radiation passing in a normal direction through the layer,
what is the ratio as a function of T1, T2, and L?
The temperature range T2 to T1 is low enough that emission from
the gas can be neglected, and the gas constant is R.

16. RADIATIVE HEAT TRANSFER
GAS RADIATION
DIMENSIONAL ARGUMENTS
1) THIN GAS
INTRODUCE
, PLANCK NUMBER
THEN
PLANCK MEAN OPTICAL THICKNESS
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

17. RADIATIVE HEAT TRANSFER
GAS RADIATION
2) THICK GAS
INTRODUCE
, ROSSELAND MEAN OPTICAL THICKNESS
THEN
HOW TO INTERPRET THIN GAS AND THICK GAS TOGETHER?
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

18. RADIATIVE HEAT TRANSFER
GAS RADIATION
INTRODUCE
THEN
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

19. RADIATIVE HEAT TRANSFER
GAS RADIATION
INTRODUCE
, GEOMETRIC MEAN OPTICAL THICKNESS
THIN GAS DESCRIBED BY
THICK GAS BY
FOR AN ARBITRARY OPTICAL THICKNESS, BY INSPECTION.
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

20. RADIATIVE HEAT TRANSFER
GAS RADIATION
thin
thick
FOR ANY OPTICAL THICKNESS
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

21. RADIATIVE HEAT TRANSFER
GAS RADIATION
thin
thick
FOR ANY OPTICAL THICKNESS
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

22. RADIATIVE HEAT TRANSFER
GAS RADIATION
FOR ANY OPTICAL THICKNESS (ENTIRE SPECTRUM)
CONSIDER
INTEGRATE OVER AND
RECALL
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

23. RADIATIVE HEAT TRANSFER
GAS RADIATION
INTRODUCE
UNDER LOCAL EQUILIBRIUM,
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

24. RADIATIVE HEAT TRANSFER
GAS RADIATION
(REF.1 S&H, CH.14, P.697
EQ.14-36, 14-42, 14-64)
THEN ①
CAN BE APPLIED FOR THE EMISSION TERM IN A GAS OF ANY OPTICAL THICKNESS. (S&H, P.745) EQ.(1) IS TRUE FOR AN ISOTROPIC SCATTERING. BUT J IS A FUNCTION OF SCATTERING. EQ.(1) IS ALSO TRUE FOR AN ANISOTROPIC SCATTERING INDEPENDENT OF INCIDENCE ANGLE (RANDOMLY ORIENTED PARTICLES).
MULTIPLY TRANSFER EQUATION BY
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

25. RADIATIVE HEAT TRANSFER
GAS RADIATION
INTEGRATE OVER AND
INTRODUCE
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

26. RADIATIVE HEAT TRANSFER
GAS RADIATION
FOR ANY OPTICAL THICKNESS
FOR OPTICALLY THICK MEDIUM OR
(REF.1 S&H) P.766, EQ.15-82
SO THAT
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

27. RADIATIVE HEAT TRANSFER
GAS RADIATION
FOR GRAY GAS
( : INDEPENDENT OF )
(S&H, P.767)
THEN ②
FOR ISOTROPIC CONDITION ③
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

28. RADIATIVE HEAT TRANSFER
GAS RADIATION ② ③
ELIMINATE BETWEEN ② AND ③ ④
FOR GENERAL
THERMOMECHANICS OF
FOR ISOTROPIC GRAY GAS ⓞ
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

29. RADIATIVE HEAT TRANSFER
GAS RADIATION ⓞ ① ④
NOW, ELIMINATE J BETWEEN ① AND ④
OR, INSERT ④ INTO ⓞ, AND ELIMINATE BETWEEN ① AND ④
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

30. RADIATIVE HEAT TRANSFER
GAS RADIATION
NOTE THAT FOR 1D PROBLEMS, AND FORMULATIONS ARE OF SIMILAR COMPLEXITY. HOWEVER, FOR 3D PROBLEMS, FORMULATION (CONSISTING OF TWO SCALAR EQUATIONS) IS MORE CONVENIENT THAN FORMULATION
(CONSISTING OF FOUR SCALAR EQUATIONS).
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

31. RADIATIVE HEAT TRANSFER
GAS RADIATION
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

32. RADIATIVE HEAT TRANSFER
GAS RADIATION
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER

33. RADIATIVE HEAT TRANSFER
GAS RADIATION
PROPULSION AND COMBUSTION LABORATORY
RADIATIVE HEAT TRANSFER