Consider the heat equation dT/dt - aΔT + v⋅∇T = S where S is a source term dependent of the radiation intensity I and the temperature T. The fluid velocity v is prescribed. We also consider the radiative transfer equation describing the radiative intensity I(x,ω,t) where ω is the ray direction. The boundary Γ consists of three parts: solid walls Γ1, inflow part Γ2 and outflow part Γ3. The domain Ω may be, for example, a rectangular channel. What boundary conditions for T should we specify on Γ2 and Γ3? What BCs are the most natural? Please give a reference if possible. What boundary conditions can be specified for I on these parts?