Radiation heat transfer can occur within porous media in conjunction with conduction, as heat is radiatively transferred across pores of interstitial fluid. Under certain conditions, the effects of such internal radiation can be approximated in terms of an effective thermal conductivity due to both conduction and radiation, \(k_{\text {eff }, r+c}=k_{\text {eff, }, c}+\sigma T^{3}\) where \(\sigma\) is the Stefan-Boltzmann constant, \(T\) is the local absolute temperature within the medium, and \(k_{\text {eff, }, ~}\) is the effective thermal conductivity of the medium due to conduction in the medium's solid and fluid phases, as described in Section 3.1.5. Consider an \(L=100 \mathrm{~mm}\) thick planar porous medium characterized by \(k_{\text {eff, }, ~}=4.0 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Using a grid spacing of \(\Delta x=10 \mathrm{~mm}\), calculate the nodal temperatures and the heat flux through the wall for surface temperatures of \(T_{s, 1}=800 \mathrm{~K}\) and \(T_{s, 2}=400 \mathrm{~K}\). Is the effect of internal radiation significant?