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

$$dE_- = -p(T)\,dt = -\sigma\,A\,T^4\,dt$$

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

$$dE_+ = p_0\,dt$$

Then you are looking for

$$dE_- + dE_+ = 0$$

Correct?

 

[abbasranjbar]

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

 

[tom.stoer]

OK, you have

$$dE_+ + dE_- = 0$$
$$p_0\,dt - \sigma\,A\,T^4\,dt = 0$$
$$p_0 = \sigma\,A\,T^4$$

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