# A radiative heat transfer problem

1. Jan 12, 2012

### bearcharge

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

q = ε.σ.T4.A.Fij

3. The attempt at a solution

I have problem identifying the view factor in this case. Can anyone help me? Thanks.

2. Jan 13, 2012

### LawrenceC

What is a semi-infinite surface dimensionwise?

3. Jan 13, 2012

### bearcharge

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. Jan 13, 2012

### LawrenceC

"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. Jan 13, 2012

### bearcharge

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. Jan 13, 2012

### LawrenceC

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. Jan 13, 2012

### bearcharge

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. Jan 13, 2012

### LawrenceC

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. Jan 13, 2012

### bearcharge

Thank you so much for the answer!