Calculating Heat Transfer Rate from a Smoky Layer to a Compartment Floor"

In summary, the problem involves calculating the rate of heat transfer from a smoky layer with dimensions 7m x 10m and a mean emissivity of 0.45 at 440°C to a homogenous/flat plate floor at 40°C, with a distance of 1.85m between them. The solution involves using the formula for heat transfer rate, substituting in the known values and solving for the unknown factor F12. Once F12 is calculated, it can be substituted into the heat transfer rate equation to find the final answer. The area of the smoky layer, A, is included in the calculations.
  • #1
Eva Brain
22
0

Homework Statement



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?

Homework Equations



yXap0.jpg


The Attempt at a Solution



Really don't know where to start from.
 
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  • #2
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
OK, I have no idea how to even start it? Any help from where to begin?
 
  • #4
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
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
Yes, that's correct. What kind of temperatures do you have to use with radiation problems?
 
  • #7
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?
 
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  • #8
SteamKing said:
Yes, that's correct. What kind of temperatures do you have to use with radiation problems?

I don't understand Q.?
 
  • #9
Eva Brain said:
I don't understand Q.?

What temperature scale must you use for radiation problems?
 
  • #10
Eva Brain said:
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?

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
I have got 0.64. From here where to go now?
 
  • #12
Eva Brain said:
I have got 0.64. From here where to go now?

For what? It would be better to show your calculations.
 
  • #13
SteamKing said:
For what? It would be better to show your calculations.

F_1,2 I have inserted everything into given formula and got the result.
 
  • #14
Now, you substitute F12 into the equation for the heat transfer rate Q.
 
  • #15
steamking said:
now, you substitute f12 into the equation for the heat transfer rate q.

Ok. One thing concerns me here and that is thinking about whether or not A is here included as radiation constant?
 
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  • #16
Yes, A is the area of the layer which is radiating the heat. Its dimensions are given in the problem statement.
 
  • #17
SteamKing said:
Yes, A is the area of the layer which is radiating the heat. Its dimensions are given in the problem statement.

Thank you I have solved it!
 

Related to Calculating Heat Transfer Rate from a Smoky Layer to a Compartment Floor"

1. How is the heat transfer rate from a smoky layer to a compartment floor calculated?

The heat transfer rate from a smoky layer to a compartment floor is calculated using the following formula:
Q = h * A * (T1 - T2)
Where Q is the heat transfer rate, h is the convective heat transfer coefficient, A is the area of the compartment floor, and T1 and T2 are the temperatures of the smoky layer and the compartment floor, respectively.

2. What factors affect the heat transfer rate from a smoky layer to a compartment floor?

The heat transfer rate from a smoky layer to a compartment floor is affected by factors such as the temperature difference between the smoky layer and the compartment floor, the size and shape of the compartment, the properties of the materials in the compartment, and the presence of any obstructions or ventilation openings.

3. Can the heat transfer rate be accurately calculated for all types of fires?

The heat transfer rate from a smoky layer to a compartment floor can be accurately calculated for most types of fires. However, for fires with highly irregular combustion or severe turbulence, the calculation may not be as accurate.

4. How does the heat transfer rate from a smoky layer to a compartment floor affect fire behavior?

The heat transfer rate from a smoky layer to a compartment floor can significantly impact fire behavior, as it determines how quickly heat is transferred from the fire to the compartment floor. This can affect the rate of fire spread and the potential for flashover or other dangerous fire behavior.

5. Are there any limitations to calculating heat transfer rate from a smoky layer to a compartment floor?

There are some limitations to calculating the heat transfer rate from a smoky layer to a compartment floor, as it is based on theoretical models and assumptions. It may not accurately reflect real-world fire scenarios, and the calculation may not be as accurate for fires with complex or changing fire behavior.

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