Difference Between Internal and External Emissivity

What is the difference between internal and external emissivity?

The external emissivity is a thermal boundary condition and does not need any kind of radiation model as it is only used for calculating the heat flux from the outer boundaries of your domain and the environment. The only exception are semi transparent external walls with the DO radiation model - in this case it is used for computing the radiation heat flux between your domain and the outer environment. In all cases you have a corresponding external radiation temperature.

The internal emissivity is used in combination with radiation models for calculating the radiation inside the domain.

Values for emissivities are between 0 (ideal mirror, every incoming radiation is reflected, no radiation is emitted) and 1 (black body, every incoming radiation is absorbed). The values depend on the material and on how the surface was machined (e. g. polished).