Finite Element Formulation of Nonlinear Thermal Conductivity Problems with Applications to Nuclear Fusion

  1. Miguel Palomino Cobo, José
  2. Palma Guerrero, Roberto
  3. Esther Puertas García, María
  4. Gallego Sevilla, Rafael
Book:
Current Research in Thermal Conductivity

ISBN: 9781837697571 9781837697564

Year of publication: 2025

Type: Book chapter

DOI: 10.5772/INTECHOPEN.1008442 GOOGLE SCHOLAR lock_openOpen access editor

Bibliographic References

  • Jiji LM. Non-Linear Conduction Problems. Berlin, Heidelberg: Springer Berlin Heidelberg; 2009. pp. 215-235. DOI: 10.1007/978-3-642-01267-9_7
  • Palma R, Pérez-Aparicio JL, Taylor RL. Non-linear finite element formulation applied to thermoelectric materials under hyperbolic heat conduction model. Computer Methods in Applied Mechanics and Engineering. 2012;213-216:93-103. Available from: https://www.sciencedirect.com/science/article/pii/S0045782511003574
  • Palma R, Moliner E, Pérez-Aparicio JL. Elasto-thermoelectric beam formulation for modeling thermoelectric devices. Finite Elements in Analysis and Design. 2017;129:32-41
  • Forner-Escrig J, Mondragon R, Hernandez L, Palma R. Non-linear finite element modelling of light-to-heat energy conversion applied to solar nanofluids. International Journal of Mechanical Sciences. 2020;188:105952
  • Forner-Escrig J, Palma R, Mondragón R. Finite element formulation to study thermal stresses in nanoencapsulated phase change materials for energy storage. Journal of Thermal Stresses. 2020;43(5):543-562
  • Palma R, Moliner E, Forner-Escrig J. Computational Thermoelectricity Applied to Cooling Devices. In: Aranguren P, editor. Bringing Thermoelectricity into Reality. Vol. 13. Rijeka: IntechOpen; 2018
  • IFMIF/EVEDA. High Flux Test Module. 2016. Available from: https://www.ifmif.org/high-flux-test-module/
  • Baluc N, Gelles D, Jitsukawa S, Kimura A, Klueh R, Odette G, et al. Status of reduced activation ferritic/martensitic steel development. Journal of Nuclear Materials. 2007;367:33-41
  • Álvarez I, Anguiano M, Mota F, Hernández R, Qiu Y. Neutronic assessment of the IFMIF-DONES HFTM specimen stack distribution. Fusion Engineering and Design. 2024;200:114212. Available from: https://www.sciencedirect.com/science/article/pii/S0920379624000656
  • Gordeev S, Schwab F, Arbeiter F, Qiu Y. Numerical study of conjugated heat transfer for DONES high flux test module. Fusion Engineering and Design. 2019;09:146
  • Mergia K, Boukos N. Structural, thermal, electrical and magnetic properties of Eurofer 97 steel. Journal of Nuclear Materials. 2008;373(1):1-8. Available from: https://www.sciencedirect.com/science/article/pii/S0022311507006642
  • Zienkiewicz OC, Taylor RL, Zhu JZ. The Finite Element Method: Its Basis and Fundamentals. Oxford, UK: Butterworth-Heinemann; 2005
  • Lax PD. Hyperbolic Partial Differential Equations. Vol. 14. Providence, Rhode Island, USA: American Mathematical Society; 2006
  • Mercier B. An Introduction to the Numerical Analysis of Spectral Methods. New York, NY, USA: Springer; 1989
  • Taylor R, Govindjee S. FEAP—A finite element analysis program, Theory Manual. Berkeley, California, USA: University of California at Berkeley, USA; 2020. Available from: http://projects.ce.berkeley.edu/feap/theory 86.pdf
  • Taylor R, Govindjee S. FEAP—A finite element analysis program, Programmer Manual. Berkeley, California 94720-1710: University of California at Berkeley, USA; 2020. Available from: http://projects.ce.berkeley.edu/feap/pmanual 86.pdf
  • Press WH. Numerical recipes 3rd edition: The art of scientific computing. Cambridge, UK: Cambridge University Press; 2007
  • Taylor R, Govindjee S. FEAP—A finite element analysis program, User Manual. Berkeley, California, USA: University of California at Berkeley, USA; 2020. Available from: http://projects.ce.berkeley.edu/feap/manual 86.pdf
  • Hesthaven JS, Warburton T. Nodal discontinuous Galerkin methods: algorithms, analysis, and applications. New York, NY, USA: Springer Science and Business Media; 2007
  • Sun W, Ma H, Qu W. A hybrid numerical method for non-linear transient heat conduction problems with temperature-dependent thermal conductivity. Applied Mathematics Letters. 2024;148:108868
  • Betz W, Papaioannou I, Straub D. Bayesian post-processing of Monte Carlo simulation in reliability analysis. Reliability Engineering System Safety. 2022;227:108731. Available from: https://www.sciencedirect.com/science/article/pii/S0951832022003544