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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, March 2, 2018 - 12:00 to 13:00

Location:

STAG 110

Event Link:

Guest Speaker:

Institution:

Radiation Transport and Reactor Physics Research Group, School of Nuclear Science and Engineering

Abstract:

Accurate knowledge of material properties in nuclear fuel is an important component to the safe, controlled operation of a nuclear reactor. Doppler broadening of neutron cross sections and heat transfer from the fuel into the coolant are directly affected by the temperature distribution. Conventionally, heat transfer follows the empirical law of Fourier, but is a macroscopic law and does not have a mechanistic connection to underlying heat transfer processes. In materials undergoing fission such as uranium dioxide, isotopic byproducts are constantly generated and affect thermal conductivity at a microscopic level. The presence of these byproducts affects the transport behavior of phonons, which are the dominant energy carriers in insulating materials.

We describe our progress in modeling and predicting thermal conductivity and temperature gradients in real materials. We employ the code Rattlesnake, a neutron transport code which solves the Boltzmann transport equation in a self-adjoint angular flux formulation, which we have modified to simulate phonon transport. We perform a frequency-dependent calculation of the phonon radiance and its angular moments, and compute thermal conductivity in silicon. Our simulations capture the processes occurring over an entire phonon frequency spectra using material properties obtained directly from first-principle, density functional theory simulations.