A nonlinear, first-order ordinary differential equation that involves Fourier-Bessel series terms has been derived to model the time-dependent motion of the solid-liquid interface during melting and solidification of a material with constant internal heat generation in cylindrical coordinates. The model is valid for all Stefan numbers. One of the primary applications of this problem is for a nuclear fuel rod during meltdown. The numerical solutions to this differential equation are compared to 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 model presented in this paper contains exponentially decaying terms in the form of Fourier-Bessel series for the temperature gradients in both the solid and liquid phases. 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.
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2018 26th International Conference on Nuclear Engineering
July 22–26, 2018
London, England
Conference Sponsors:
- Nuclear Engineering Division
ISBN:
978-0-7918-5148-7
PROCEEDINGS PAPER
Fourier-Bessel Series Model for the Stefan Problem With Internal Heat Generation in Cylindrical Coordinates
Lyudmyla Barannyk,
Lyudmyla Barannyk
University of Idaho, Moscow, ID
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John Crepeau,
John Crepeau
University of Idaho, Moscow, ID
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Patrick Paulus,
Patrick Paulus
University of Idaho, Moscow, ID
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Ali Siahpush
Ali Siahpush
Southern Utah University, Cedar City, UT
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Lyudmyla Barannyk
University of Idaho, Moscow, ID
John Crepeau
University of Idaho, Moscow, ID
Patrick Paulus
University of Idaho, Moscow, ID
Ali Siahpush
Southern Utah University, Cedar City, UT
Paper No:
ICONE26-81009, V06AT08A002; 7 pages
Published Online:
October 24, 2018
Citation
Barannyk, L, Crepeau, J, Paulus, P, & Siahpush, A. "Fourier-Bessel Series Model for the Stefan Problem With Internal Heat Generation in Cylindrical Coordinates." Proceedings of the 2018 26th International Conference on Nuclear Engineering. Volume 6A: Thermal-Hydraulics and Safety Analyses. London, England. July 22–26, 2018. V06AT08A002. ASME. https://doi.org/10.1115/ICONE26-81009
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