Rate of heat transfer

1. Mar 10, 2014

Eva Brain

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

The underside of a smoky layer 7m x 10m is radiating like a flat, isotropic plate at 440°C to the floor of a compartment 1.85m below. The mean emissivity is 0.45 and the floor is homogenous/flat plate at 40°C. What is the rate of heat transfer from the smoky layer to the floor?

2. Relevant equations

3. The attempt at a solution

Really don't know where to start from.

2. Mar 10, 2014

SteamKing

Staff Emeritus
Why don't you start by plugging in the known information from the problem statement into the formulas you were given. At least that will show you have tried to solve the problem rather than immediately giving up.

3. Mar 10, 2014

Eva Brain

OK, I have no idea how to even start it? Any help from where to begin?

4. Mar 10, 2014

SteamKing

Staff Emeritus
In the diagram attached to the OP, which would be the ceiling and which would be the floor? What are the temperatures of the two? (Hint: TH - hot temperature and TC - cold temperature)

5. Mar 10, 2014

Eva Brain

A_1 is the ceiling, A_2 is the floor. A_1 has TH of 440 degrees, and A_2 has TC of 40 degrees?

6. Mar 10, 2014

SteamKing

Staff Emeritus
Yes, that's correct. What kind of temperatures do you have to use with radiation problems?

7. Mar 10, 2014

Eva Brain

I have calculated following X = 3.78 and Y = 5.40

Having this now I have tried to calculate F_1,2! I get following result 2/3671.16^degrees ( 1.16 + 1135.0^degrees).

From here I don't know how to compute integeres and degrees? Should I convert this all to pi value, ie 1135.0^degrees is 6.03PI?

Last edited: Mar 10, 2014
8. Mar 10, 2014

Eva Brain

I don't understand Q.?

9. Mar 10, 2014

SteamKing

Staff Emeritus
What temperature scale must you use for radiation problems?

10. Mar 10, 2014

SteamKing

Staff Emeritus
It's not clear what you've done here. Hint: not all arguments for trig functions have to be expressed in degrees. Here, radians is appropriate. The quantities X and Y are already non-dimensionalized.

Be sure you set your calculator to 'Radian' mode before doing your calculations. F12 is, I suspect, a factor related to the geometry of the compartment, and probably doesn't have units.

11. Mar 11, 2014

Eva Brain

I have got 0.64. From here where to go now?

12. Mar 11, 2014

SteamKing

Staff Emeritus
For what? It would be better to show your calculations.

13. Mar 11, 2014

Eva Brain

F_1,2 I have inserted everything into given formula and got the result.

14. Mar 11, 2014

SteamKing

Staff Emeritus
Now, you substitute F12 into the equation for the heat transfer rate Q.

15. Mar 11, 2014

Eva Brain

Ok. One thing concerns me here and that is thinking about whether or not A is here included as radiation constant?

Last edited: Mar 11, 2014
16. Mar 11, 2014

SteamKing

Staff Emeritus
Yes, A is the area of the layer which is radiating the heat. Its dimensions are given in the problem statement.

17. Mar 12, 2014

Eva Brain

Thank you I have solved it!