A radiative heat transfer problem

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SUMMARY

The forum discussion centers on calculating net radiative heat fluxes for a firefighter approximated as a two-sided black surface at 310 K, facing a semi-infinite black surface fire at 1500 K. Key equations include q = ε.σ.T4.A.Fij, where the view factor is crucial for accurate calculations. Participants emphasize the importance of flame thickness and its effect on emissivity, particularly for gases like CO2 and H2O. The discussion also highlights the need for shape factor tables to determine configuration factors between the firefighter, the ground, and the flames.

PREREQUISITES
  • Understanding of radiative heat transfer principles
  • Familiarity with the Stefan-Boltzmann law
  • Knowledge of view factors and shape factors in thermal radiation
  • Basic concepts of emissivity and its dependence on material properties
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  • Research "View Factor Calculations in Radiative Heat Transfer"
  • Study "Shape Factor Tables for Various Geometries"
  • Explore "Emissivity of Gases in Radiative Heat Transfer"
  • Learn about "Stefan-Boltzmann Law Applications in Engineering"
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Engineers, physicists, and students specializing in thermal engineering, heat transfer analysis, and fire safety design will benefit from this discussion.

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Homework Statement



A fire fighter (approximated by a two-sided black surface at 310 K 180 cm long and 40 cm wide) is facing a large fire at a distance of 10 m (approximated by a semi-infinite black surface at 1500 K). Ground and sky are at 0 °C (and may also be approximated as black). What are the net radiative heat fluxes on the front and back of the fire fighter?

Homework Equations



q = ε.σ.T4.A.Fij

The Attempt at a Solution



I have problem identifying the view factor in this case. Can anyone help me? Thanks.
 
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What is a semi-infinite surface dimensionwise?
 
LawrenceC said:
What is a semi-infinite surface dimensionwise?

my understanding is the wall is extending to infinity both in width and in height. But as the wall is standing on the ground, that's where the 'semi' comes from. By the way, the thickness doesn't make a difference as radiation is mainly concerned about surface.
 
"By the way, the thickness doesn't make a difference as radiation is mainly concerned about surface."

Actually thickness is quite important when it is a sheet of flame (gas radiation) with no solid wall behind it. The emissivity is a function of flame thickness. CO2 and H20 are good emitters.

Can you determine the configuration factor between the fireman and the ground in front of him, then use factor algebra to determine the factor for the flame?
 
LawrenceC said:
"By the way, the thickness doesn't make a difference as radiation is mainly concerned about surface."

Actually thickness is quite important when it is a sheet of flame (gas radiation) with no solid wall behind it. The emissivity is a function of flame thickness. CO2 and H20 are good emitters.

Can you determine the configuration factor between the fireman and the ground in front of him, then use factor algebra to determine the factor for the flame?

I'm sorry but I don't know how to determine the configuration factor between the fireman and the ground. I was also wondering how to treat the sky?
 
One side of him is exposed to the flames and ground, both of which are semi-infinite planes. The other side sees only the ground and sky so its shape factor would be unity.

Do you have a textbook that provides shape factor formula tables for differing geometries? For instance, a small area dA (infintesimal) at a distance from a finite area either looking directly at it (flame) or looking 90 degrees from it (ground). Dimensions of the finite rectangle would be 'a' wide and 'b' long. The distance dA from the rectangle would be 'c'. The shape factors are then provided in terms of ratios of the dimensions.
 
LawrenceC said:
One side of him is exposed to the flames and ground, both of which are semi-infinite planes. The other side sees only the ground and sky so its shape factor would be unity.

Do you have a textbook that provides shape factor formula tables for differing geometries? For instance, a small area dA (infintesimal) at a distance from a finite area either looking directly at it (flame) or looking 90 degrees from it (ground). Dimensions of the finite rectangle would be 'a' wide and 'b' long. The distance dA from the rectangle would be 'c'. The shape factors are then provided in terms of ratios of the dimensions.

Thank you for pointing this one out. I do have a textbook for reference. But I was wondering if I assume the view factor of fireman to wall be 0.5 as if the wall is extending in the opposite direction, this would make it 'infinite' and the factor would be 1, so dividing by two according to symmetry the original factor would be 0.5.
 
Don't forget about the heat exchange with the ground. Some thermal energy is lost on that exchange (fireman's front).

The parameterized equations for the factors I have access to predict a factor of 0.5 to the flames.
 
LawrenceC said:
Don't forget about the heat exchange with the ground. Some thermal energy is lost on that exchange (fireman's front).

The parameterized equations for the factors I have access to predict a factor of 0.5 to the flames.

Thank you so much for the answer!
 

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