# Engineering Physics Colloquium

Tuesday, October 23

4:00 PM to 5:00 PM

106 Engineering Research Building

**Speaker: ** Dr. Barry D. Ganapol, University of Arizona

"The Analytical Solution to the 1D Multigroup Diffusion Equation in Heterogenous Media"

**Abstract:** The analytical solution to the time-independent multigroup diffusion equation in heterogeneous plane, cylindrical and spherical media will be presented. The solution features the simplicity of the one-group formulation while addressing the complication of multigroup diffusion in a fully heterogeneous medium. Beginning with the vector form of the diffusion equation, the approach, based on straightforward mathematics, resolves a set of coupled second order ODEs. The analytical form is facilitated through matrix diagonalization of the neutron interaction matrix rendering the multigroup equation as a series of one-group equations. Customized eigenmode solutions of the one-group diffusion operator then represent the homogeneous solution in a homogeneous region. Once the homogeneous solution is known, the particular solution naturally emerges through variation of parameters. The analytical expression is numerically implemented through recurrence. We end with applications to the 1D/C5G7 MOX benchmark and an Advanced Test Reactor (ATR) fuel plate.

**Biography:** Dr. Ganapol currently works at the Department of Aerospace and Mechanical Engineering at the University of Arizona in Tuscon, AZ. He earned his Ph.D. in 1971 from the University of California, Berkeley. Barry Ganapol's research interests include radiation and particle transport theory, fast reactor safety, applied mathematics, and satellite remote sensing.

**Event Note:** 3:45pm refreshments will be served.