IGNOU MPHE 26 2026 - Derive two-group diffusion equations for a critical homogeneous reacto

Question

Derive two-group diffusion equations for a critical homogeneous reactor in steady state.

19 Jan 2026

Answer :

Word Count : 363

For a homogeneous reactor in steady state, we consider a two-group neutron diffusion model with fast ((1)) and thermal ((2)) neutrons. Let ( \phi_1 ) and ( \phi_2 ) be the neutron fluxes for the fast and thermal groups, ( D_1, D_2 ) the diffusion coefficients, ( \Sigma_{a1}, \Sigma_{a2} ) the absorption cross-sections, and ( \Sigma_{s12} ) the scattering cross-section from fast to thermal neutrons. Let ( \nu \Sigma_{f1}, \nu \Sigma_{f2} ) denote the production rates of neutrons by fission in each group. The general diffusion equation in steady state is: [ * D_g \nabla^2 \phi_g + \Sigma_{ag} \phi_g = S_g ] where (S_g) is the neutron source in group (g). Step 1: Fast group equation Fast neutrons are produced by fission in both groups and lost by absorption or slowing down to the thermal group: [ * D_1 \nabla^2 \phi_1 + \Sigma_{a1} \phi_1 +

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