maximum temperature under radiation

abbasranjbar

Hello everyone,
As you all know, the temperature of a metal increases under electromagnetic radiation. The metal also has a black body radiation which decreases its temperature. There is an equilibrium temperature which is the maximum temperature of the metal under the radiation. I am looking for formulas or publication that gives me this final temperature.

Thanks

tom.stoer

Hm, it seems you want to calculate the net energy flow with

[tex]dE_- = -p(T)\,dt = -\sigma\,A\,T^4\,dt[/tex]

where p(T) is the integrated density from Stefan-Boltzmann, and from an external radiation source with

[tex]dE_+ = p_0\,dt[/tex]

Then you are looking for

[tex]dE_- + dE_+ = 0[/tex]

Correct?

abbasranjbar

Yes, actually the equilibrium T of the material because of this net energy.

tom.stoer

OK, you have

[tex]dE_+ + dE_- = 0[/tex]
[tex]p_0\,dt - \sigma\,A\,T^4\,dt = 0[/tex]
[tex]p_0 = \sigma\,A\,T^4 [/tex]

So the temperature is constant iff the black body radiation is balanced by radiation received from the external source.

abbasranjbar

Thank you Tom.
That makes sense. I checked it couple of times and my results were not match with the publications. I will check again to find the reason of the difference.

Cheers