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On the Radiative Conductive Transfer Equation: A Heuristic Convergence Criterion by Stability Analysis

In: Integral Methods in Science and Engineering, Volume 1

Author

Listed:
  • C. A. Ladeia

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

  • J. C. L. Fernandes

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

  • B. E. J. Bodmann

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

  • M. T. Vilhena

    (Federal University of Rio Grande do Sul, Department of Mechanical Engineering)

Abstract

Recently, the radiative conductive transfer equation in cylinder geometry was solved in semi-analytical fashion by the collocation method in both angular variables, using the S N procedure. Upon application of the decomposition method the resulting recursive system of S N radiative transfer equations was evaluated by the Laplace transform technique considering the non-linear term as source. In the present work we prove a heuristic convergence of the discussed solution inspired by stability analysis criteria and taking into account the influence of the parameter sets. Finally, we report on some case studies with numerical results for the solutions and convergence behaviour.

Suggested Citation

  • C. A. Ladeia & J. C. L. Fernandes & B. E. J. Bodmann & M. T. Vilhena, 2017. "On the Radiative Conductive Transfer Equation: A Heuristic Convergence Criterion by Stability Analysis," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 0, pages 173-182, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59384-5_15
    DOI: 10.1007/978-3-319-59384-5_15
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