CONVERGENCE PROOF OF A TEMPERATURE-BASED FINITE ELEMENT FORMULATION FOR TRANSIENT HEAT TRANSFER

Authors

  • Jacqueline Elhage Ramis ITA
  • Paulo Ivo Braga de Queiroz
  • Eliseu Lucena Neto ITA
  • Alex Guimarães de Azevedo ITA
  • Paulo Scarano Hemsi ITA

DOI:

https://doi.org/10.26512/ripe.v2i12.21340

Keywords:

Convergence. Eigenvalue bound. Finite element. Heat conduction.

Abstract

A finite element is developed to discretize spatially one-dimensional transient heat conduction problems in both space and time. Stability of the recursive discretized equation is proved using the eigenvalues of the amplification matrix. Convergence, in this case, stems naturally from the formulation consistency of the developed finite element. Numerical experiments demonstrate that refined models are in close agreement with the exact solution.

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References

Al-Khoury, R., 2012, Computational modeling of shallow geothermal systems, CRC Press, Boca Raton.

Barry, B., 2002, Transdermal drug delivery, in M. E. Aulton (ed.), Pharmaceutics: the science of dosage form design, 2nd edn, Churchill Livingstone, Edinburgh, chapter 33, pp. 499”“533.

Bergman, T. L., Lavigne, A. S., Incropera, F. P. & Dewitt, D. P., 2011, Fundamentals of Heat and Mass Transfer, 7th edn, John Wiley & Sons, Hoboken, NJ.

Fish, J. & Belytschko, T., 2007, A first course in finite element, John Wiley, Chichester.

Irons, B. M. & Treharne, G., 1971, A bound theorem in eigenvalues and its practical applications, Proceedings of the Third Conference on Matrix Methods in Structural Mechanics, Wright Patterson Air Force Base, Ohio, pp. 245”“254. Available at http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0785968.

Lambe, W. T. & Whitman, R. V., 1969, Soil Mechanics, John Wiley & Sons, New York.

Lax, P. D. & Richtmyer, R. D., 1956, Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math., vol. 9, pp. 267”“293.

Reddy, J. N., 2006, An introduction to the finite element method, 3rd edn, McGraw-Hill, Boston.

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Published

2017-01-10

How to Cite

Ramis, J. E., Queiroz, P. I. B. de, Lucena Neto, E., Azevedo, A. G. de, & Hemsi, P. S. (2017). CONVERGENCE PROOF OF A TEMPERATURE-BASED FINITE ELEMENT FORMULATION FOR TRANSIENT HEAT TRANSFER. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(12), 01–10. https://doi.org/10.26512/ripe.v2i12.21340

Issue

Vol. 2 No. 12 (2016): COMPUTATIONAL THERMAL SCIENCES

Section

Artigos

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