How to implement the radiation boundary condition for the object in vacuum?

I am trying to simulate heat transfer in the object that is mounted inside the vacuum chamber using the PDE toolbox. The thing is cooled internally with water running through the pipe inside. But I suppose that it can also loose some energy via the radiation from the boundaries into the surrounding vacuum. The question is how to program this radiative BC into vacuum correctly in Matlab using the PDE toolbox. Another question is if this radiative heat loss is even worth taking it into account, if it would be significant compared to other cooling mechanisms.

[David Goodmanson]

Hi Alexander,

for the second question you can do an approximate calculation for the size of the effect. For an object of area A, temperature T in kelvin, Tc the temperature of the walls of the vacuum chamber, and eps the emissivity (usually between 0 and 1) , from the Stefan-Boltmann law

W = 5.67e-8*eps*A*(T^4 -Tc^4)

where W is the radiated power in watts. So for example if A = 2, Tc = 296, T = 346, eps = .8, then W = 604 watts.