External Radiation to Heat Transfer Surfaces at Furnace Exit

The calculations provided earlier give an estimate of energy absorbed by the furnace. However, there will be direct radiation to heat transfer surfaces such as superheaters or boiler screen section at furnace exit. One may estimate this as follows:

The energy absorbed by furnace from Example 1 = 12,642 kW. The furnace area = 127 m 2 . The average heat flux = 99.5 kW/m 2 . Let the opening at furnace exit = 3.35 × 1.2 = 4 m 2 .

Then approximately 99.5 × 4 = 398 kW energy is radiated to the tube section at furnace exit. However, one has to correct for the actual emissivity at the furnace exit and the smaller beam length and the distribution of heat flux along the flame length. Equations and charts are available in Ref. [7] for estimating the correction factor, and it may be seen that about 0.5–0.6 times the average flux is radiated to the surfaces beyond the furnace. Hence, the direct radiation may be taken as 250 kW, and the furnace absorbs 12,642 − 250 = 12,392 kW. If the screen section is located at the furnace exit, then this radiant energy is added to the evaporator duty; thus the external radiation does not cause any concern when the screen section absorbs this radiation as the boiling coefficient inside tubes is high and does not increase the tube wall temperature much; however, when a superheater is located at the furnace exit, then this has to be considered as contributing to the superheater duty. The first few rows of tubes depending on tube spacing will receive this external radiation and can overheat the superheater tubes. The distribution of external radiation to tube bank was discussed earlier. The first four to five rows typically absorb this radiation completely with the first row bearing the maximum brunt.

If we estimate the gas emissivity at the furnace exit and compute the external radiation, we get a different value for external radiation. From Example 2.1, P c = 0.08, P w = 0.18. At the furnace exit and opening to the convection bank, the beam length is different. Using a width of 2.44 m, height = 3.35 m, and length = 1.2 m,

L = 1.7/(1/2.44 + 1/3.35 + 1/1.2) = 1.1 m.

K = (.8 + 1.6 ×.18) × (1 − 0.00038 × 1423) × (0.26)/(0.26 × 1.1) 0.5 = 0.24

∈ f = (1 − e −.24 × 1.1 ) = 0.23. Let ∈ w = 0.9

66 Steam Generators and Waste Heat Boilers: For Process and Plant Engineers

Direct radiation to furnace opening to tubes at, say, 660 K = 5.67 × 10 –11 × 0.23 × 0.9 × (1423 4 − 660 4 ) × 4 = 184 kW. (Opening to furnace = 3.35 × 1.2 = 4 m 2 ) Let us say that we have located the radiant superheater at the furnace exit (not a good idea). Let there be 12 tubes of diameter 50.8 and length 3.35 m facing the furnace at a spacing of 100 mm. One can estimate the average heat flux in the furnace and the energy radiated at the furnace exit as discussed earlier and compute the energy absorbed row by row. The fraction a absorbed by the first row is given by

a = 3.14 (d/2S) − d/S[sin −1 (d/S) + {(S/d) 2 − 1} 0.5 − S/d] For a S T /d = 2, a = 3.14/4 – 0.5 × [sin −1 (0.5) + 30 0.5 − 2] = .785 − 0.5 × [0.523 + 1.732 − 2] = 0.66

[the value for sin -1 (0.5) is in radians]. The first row absorbs the maximum of 66% of the external radiation. Let 0.66 × 184 = 121 kW of energy be absorbed in the first row. Then the additional heat flux due to direct radiation is 121 × 860 = 104,438 kcal/h. If the steam generation is 40,000 kg/h, and there are 20 streams in 5 tubes/row (on each header) and 4 along gas path with 3 passes in

12 rows (see Figure B.4h for explanation of streams), flow through each tube will be about 2,000 kg/h. With a baffle after every 4 rows of tubes, the additional enthalpy absorbed by steam is (104,438/12/2,000) × 3 = 13 kcal/kg. Assuming steam-specific heat of 0.65 kcal/kg °C, the additional pickup in steam temperature and wall temperature can be at least 20°C. This can decrease the life of the superheater by several years if you check using the LMP charts for the material in consideration (see Appendix E). The tubes may be even operating well above their limits and can fail. Hence, locating the superheater at the furnace exit is not good practice as discussed in Chapter 3. Advantages of convective superheater design have been elaborated in Chapter 3. Due to mixing with slightly cooler steam in subsequent rows away from the furnace, the enthalpy total pickup by the first row could be slightly less but still a factor to be considered. If, for argument, we assume the first row facing the furnace starts out at 350°C and gets heated to 400°C, then this row can pick up an additional 20°C as shown and can cause overheating. Several superheaters located at furnace exit have failed for this reason. Also we estimate a particular furnace exit gas temperature. What if it

is about 50°C higher? The radiation will be about (1473/1423) 4 or 15% more, or the temperature increase is higher by 23°C.

External Radiation to Heat Transfer Surfaces at Furnace Exit