A radiative heat transfer problem

In summary, the fire fighter is approximated by a two-sided black surface at 310 K with dimensions of 180 cm by 40 cm. They are facing a large fire, approximated by a semi-infinite black surface at 1500 K, at a distance of 10 m. The ground and sky, both approximated as black, are at 0 °C. The net radiative heat fluxes on the front and back of the fire fighter can be calculated using the equation q = ε.σ.T4.A.Fij, where q is the heat flux, ε is the emissivity, σ is the Stefan-Boltzmann constant, T is the temperature, A is the surface area, and Fij
  • #1
bearcharge
28
0

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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  • #2
What is a semi-infinite surface dimensionwise?
 
  • #3
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.
 
  • #4
"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?
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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!
 

Related to A radiative heat transfer problem

1. What is radiative heat transfer?

Radiative heat transfer is the process by which heat energy is transferred through electromagnetic waves. This type of heat transfer does not require a medium, such as air or water, and can occur through a vacuum.

2. What factors affect radiative heat transfer?

The factors that affect radiative heat transfer include the temperature and properties of the emitting and receiving surfaces, the distance between the surfaces, and the presence of any intervening materials that may absorb or reflect the radiation.

3. How is radiative heat transfer quantified?

Radiative heat transfer is quantified using the Stefan-Boltzmann law, which states that the rate of heat transfer is proportional to the fourth power of the temperature difference between the two surfaces.

4. What are some real-world applications of radiative heat transfer?

Radiative heat transfer is commonly seen in everyday life, such as in the warmth we feel from the sun, the heat emitted from a fire, or the heat transfer in cooking. It is also a crucial factor in technologies such as solar panels and thermal imaging.

5. What are some challenges in solving radiative heat transfer problems?

One of the main challenges in solving radiative heat transfer problems is the complexity of the equations involved. The properties of the surfaces, as well as the geometry and boundary conditions, must also be accurately accounted for. Additionally, the use of numerical methods may be necessary for more complex scenarios.

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