maximum temperature under radiationby abbasranjbar Tags: black body, equilibrium, heat transfer, temperature, thermodynamics 

#1
Nov712, 04:36 PM

P: 4

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 



#2
Nov712, 06:06 PM

Sci Advisor
P: 5,307

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 StefanBoltzmann, and from an external radiation source with [tex]dE_+ = p_0\,dt[/tex] Then you are looking for [tex]dE_ + dE_+ = 0[/tex] Correct? 



#3
Nov712, 06:28 PM

P: 4

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




#4
Nov712, 07:44 PM

Sci Advisor
P: 5,307

maximum temperature under radiation
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. 



#5
Nov712, 08:02 PM

P: 4

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 


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