Thermal radiation transfer rate

[Hitman6267]

See attached pic

=>

<=
r=2.2
h=4.9
T= 37 Celsius
Ten= 65 Celsius
emissivity= 0.81

For the surface area I used:
A= 2 pie r^2 + 2 pie r h

I converted both r and h into meter

For the thermal radiation transfer I used the following equation

P= Stefan-boltzmann constant X emessivity X surface area X (T environment^4 - T of the
cylinder^4)

My answer is 1.72

What is my mistake ?

 

[rock.freak667]

Well without showing exactly what you did, the only place I can see where you would make a mistake is not converting from Celsius to Kelvin. Did you do that?

 

[Hitman6267]

oh sorry. I was planning on attaching an excel file with calculations. Any way here is what I did. Yes I converted from Celsius to kelvin.

P= 5.6704 x10^08 X 0.81 X 0.009814 (surface area) X (338.15^4 - 310.15^4)

 

[rock.freak667]

I don't see anything wrong in your analysis then, why do you have reason to think that is wrong?

 

[Hitman6267]

we use wiley plus and when i submited my answer it says it's wrong (there's a 3% tolerance). But I think you can agree that there is nothing wrong with my answer - I calculated it multiple times before posting here.

 

[Mapes]

Your S-B constant and area both have a problem with decimal position. How did you calculate the second area? I get a P2/P1 ratio between 2 and 3.

 

[D H]

My answer is 1.72

1.72 what? Failing to specify the units that a result is in is a common mistake. Failing to recognize that there are multiple systems of units is another. Note for example that the length of the cylinder is specified as 4.9 centimeters, not just 4.9. Units are very important. "Don't leave home without them."

What is my mistake ?

My guess: Units.

 

[Hitman6267]

@Mapes
I copied the S-B constant from my book and I verified my area with an online area calculator.

P2/P1 = 2.75 (I got it right)

@D H
1.72W
I didn't mention the units because they are clearly stated in the screen shot I attached.

 

[Mapes]

@Mapes
I copied the S-B constant from my book and I verified my area with an online area calculator.

P2/P1 = 2.75 (I got it right)

Got it - was [itex]\sigma=5.67\times 10^{8}\,\mathrm{W}\,\mathrm{m}^{-2}\,\mathrm{K}^{-4}[/tex] a typo? (Should be [itex]5.67\times 10^{-8}\,\mathrm{W}\,\mathrm{m}^{-2}\,\mathrm{K}^{-4}[/tex].) I goofed on the area. And I concur with your final answer.

 

[Hitman6267]

Oh sorry about that, I didn't notice it. So there isn't something I missed ? This is frustrating I've been over it a million times and I always get the same answer.

I asked a friend of mine to get the person he did for him to do mine. He got -1.72 and it is correct. Why is that ?

 

[Mapes]

This is the problem with not using units. The whole time I thought that you were getting a ratio (not a power) of 1.72 because you didn't add the "W" after it.

The answer key is using the convention that net output power is positive. This is an arbitrary choice.

 

[Hitman6267]

oh I apologize, I'll avoid doing that in the future.

Could you elaborate on what you said about the convention?
All I know that the transfer rate is:
P= Stefan-boltzmann constant X emessivity X surface area X (T environment^4 - T of the cylinder^4

Where does a convention come in ?

 

[D H]

The convention is which of an outward versus inward net heat transfer is designated as positive versus negative.

 

[Hitman6267]

But where does that come in the formula
P= Stefan-boltzmann constant X emessivity X surface area X (T environment^4 - T of the cylinder^4)

Edit: I reread the chapter in my book and I found a small part that describes when its positive and when it's negative.

But there isn't anything in the question that tells us if the boding is absorbing or emitting the radiation.

A solid cylinder of radius r1 = 2.2 cm, length h1 = 4.9 cm, emissivity 0.81, and temperature 37°C is suspended in an environment of temperature 65°C. (a) What is the cylinder's net thermal radiation transfer rate P1?

And they're asking about the transfer rate. So why would I assume it's negative

 

[Mapes]

But where does that come in the formula
P= Stefan-boltzmann constant X emessivity X surface area X (T environment^4 - T of the cylinder^4)

It doesn't appear in the formula. That's why a convention is needed.

And they're asking about the transfer rate. So why would I assume it's negative

You wouldn't, unless you knew the convention somehow. If you were never taught the convention, and it's not in your book, then the question isn't fair.