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.
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References
Boichenko, V.A., Leonov, G.A., Reitmann, V.: Dimension Theory for Ordinary Differential. Teubner, Stuttgart (2005)
Chandrasekhar, S.: Radiative Transfer. Oxford University Press, New York (1950)
Elghazaly, A.: Conductive-radiative heat transfer in a scattering medium with angle-dependent reflective boundaries. J. Nucl. Radiat. Phys. 4, 31–41 (2009)
Ladeia, C.A., Bodmann, B.E.J., Vilhena, M.T.B.: The Radiative-Conductive Transfer Equation in Cylinder Geometry and Its Application to Rocket Launch Exhaust Phenomena. Integral Methods in Science and Engineering. Springer, Cham (2015). ISBN: 978-3-319-16727-5. doi:10.1007/978-3-319-16727-5_29
Li, H.-Y.: A two-dimensional cylindrical inverse source problem in radiative transfer. J. Quant. Spectrosc. Radiat. Transf. 69, 403–414 (2000)
Li, H.Y., Ozisik, M.N.: Simultaneous conduction and radiation in a two-dimensional participating cylinder with anisotropic scattering. J. Quant. Spectrosc. Radiat. Transf. 46, 393–404 (1991)
Mishra, S. C., Krishna, Ch. H., and Kim, M. Y.: Analysis of conduction and radiation heat transfer in a 2-D cylindrical medium using the modified discrete ordinate method and the lattice Bolztmann method. Numer. Heat Transf. 60, 254–287 (2011)
Modest, M.F.: Radiative Heat Transfer. McGraw-Hill, New York (1993)
Ozisik, M.N.: Radiative Transfer and Interaction with Conductions and Convection. Wiley, New York (1973)
Pazos, R.P., Vilhena, M.T., Hauser E.B.: Advances in the solution of threedimensional nodal neutron transport equation. In: 11th International Conference of Nuclear Engineering, Tokyo (2003)
Vilhena, M.T.M.B., Bodmann, B.E.J., Segatto, C.F.: Non-linear radiative-conductive heat transfer in a heterogeneous gray plane-parallel participating medium. In: Ahasan, A. (ed.) Convection and Conduction Heat Transfer. InTech, New York (2011). ISBN: 978-953-307-582-2. doi:10.5772/22736
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Ladeia, C.A., Fernandes, J.C.L., Bodmann, B.E.J., Vilhena, M.T. (2017). On the Radiative Conductive Transfer Equation: A Heuristic Convergence Criterion by Stability Analysis. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_15
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DOI: https://doi.org/10.1007/978-3-319-59384-5_15
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