(Solved): Radiative equilibrium in a slab with uniform internal heating Please do it in detail! Consider a ...

Radiative equilibrium in a slab with uniform internal heating

Please do it in detail!

Consider a gray, homogeneous, non-scattering slab bounded by cold black walls $$\left(T_w=0K\right)$$. A uniform internal heating dissipates a volume heat source $$q_0^{???}$$ within the medium (eg, joule heating). Figure 1: Slab with a uniform internal heating between black cold walls. 1. Prove that, in this configuration, the radiative equilibrium condition is $$\frac{d{q}^{??}}{dx}=q_0^{???}$$ or $$\frac{d{q}^{??}}{d?}=\frac{d{q}_0^{???}}{{?}_a}$$ 2. Using the moment method (no need to re-demonstrate the setting up of the model calculate the distributions of the radiative flux $$q^{??}(?)$$ and of the power 4 of the temperature $$T^4(?)$$ the slab at radiative equilibrium.