Heat exchange, emissivity and reflectance

[Carlos de Meo]

Hi Guys
I´m studying the heat exchange problem in furnaces and, to begin with, i started with Incropera´s book.
One thing is actually driving me crazy
On the last part of this exercise´s solution (part 3), the physical principle involved is not very clear to me. To calculate the absorptivity of the wall, it´s assumed that emissivity = absorptivity. But, as far as i know, this is the famous Kirchhoff Law and it´s only valid when the system reaches thermal equilibrium, which is clearly not the case here. Can someone explain me what is going on?

 

[Navin A S]

The Kirchhoff Law is a general law that states that the emissivity of an object is equal to its absorptivity. This law is valid in thermal equilibrium, but it can also be used to approximate the behavior of materials in non-equilibrium situations. In this case, the wall's absorptivity is approximated by assuming that it has the same emissivity as its absorptivity. This simplification allows us to calculate the absorptivity of the wall without having to measure it directly.