Heat Transfer

[Integrator741]

Good evening chaps, this post might be a bit out of blue, but I will give it a try.

With no further ado:

"The cylindrical element of a 1.0 kW electric fire is 30cm long and 1cm in diameter. Taking the temperature of the surrounding to be 20 C and Stefan's constant to be 5.7 x 10^-8 estimate the working temperature of the element."

Answer is: 900C

I used Stefan's formula (P=AQT^4) and tried to solve for T - that didn't work out. I don't know where to go next. I understand that they give you the outside temperature, because you need to calculate "Working temperature" so that means I need to note that some temperature will dissipate, am I right?

Please help,

 

[Arouse1973]

Here are my workings. Can you see how to get the answer now?
Thanks
Adam

 

[Integrator741]

Here are my workings. Can you see how to get the answer now?
Thanks
Adam
View attachment 22839

Not really sure what you did with T there and can you please walk me through the Area calculations - thanks.

 

[duke37]

"unroll" the surface to make a rectangle. This will be pi*D by L.
pi * 0.01 * 0.300 = 0.009 m2, neglecting the ends.

 

[Arouse1973]

Not really sure what you did with T there and can you please walk me through the Area calculations - thanks.

Look carefully you should see what I have done with T. Also Trevor gave you a hint for the area calculation. Look at the two formulas and see if you can work out what's going on. Show us your calculations. It would be nice to see where your going wrong.
Thanks
Adam

 

[Integrator741]

Look carefully you should see what I have done with T. Also Trevor gave you a hint for the area calculation. Look at the two formulas and see if you can work out what's going on. Show us your calculations. It would be nice to see where your going wrong.
Thanks
Adam

Good evening,

Sorry I am late with my replay - many thanks for your help, I just understood it. (We need to unroll the damn thing to calculate the surface area - duhh...)

Thank you very much!