COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics
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Mathematics Colloquium: Modeling the Stefan problem for materials with internal heat generation in cylindrical geometry using Fourier-Bessel series


Neill 5W, 4:10pm

Lyudmyla Barannyk

We study time-dependent motion of the solid-liquid interface during melting and solidification of a material with constant internal heat generation in cylindrical geometry. We derive a nonlinear, first-order ordinary differential equation for the interface that involves Fourier-Bessel series. The model is valid for all Stefan numbers. One of the primary applications of this problem is for a nuclear fue l rod during meltdown. The numerical solutions of the initial value problem are compared with the solutions of a previously derived model that was based on the quasi-steady approximation, which is valid only for Stefan numbers less than one. The agreement between the two models is excellent in the low Stefan number regime. For higher Stefan numbers, where the quasi-steady model is not accurate, the new model differs from the approximate model since it incorporates the time- dependent terms for small times, and as the system approaches steady-state, the curves converge. At higher Stefan numbers, the system approaches steady-state faster than for lower Stefan numbers. During the transient process for both melting and solidification, the temperature profiles become parabolic. Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)