Consider the heat equation(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Boundary conditions for heat transfer in the pipe

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