IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-07171-3_12.html
   My bibliography  Save this book chapter

A Simple Numerical Scheme to Obtain Reflectivity and Transmissivity of an Isotropically Scattering Slab

In: Integral Methods in Science and Engineering

Author

Listed:
  • C. A. Ladeia

    (Federal University of Rio Grande do Sul)

  • H. R. Zanetti

    (Federal University of Rio Grande do Sul)

  • D. L. Gisch

    (Federal University of Rio Grande do Sul)

  • M. Schramm

    (Federal University of Pelotas)

  • J. C. L. Fernandes

    (Federal University of Rio Grande do Sul)

Abstract

In this chapter, we consider the linear radiative transfer model for a passive medium with no intrinsic thermal contributions. The domain is a one-dimensional slab for which reflectivity and transmissivity are determined from the total in- and outgoing radiative fluxes across the boundaries. Further, we assume isotropic scattering in the medium and no emissivity and reflectivity on the boundaries but thermal radiation from the latter and an isotropic incoming radiation from an external source. Our developments are based on the discrete ordinate method in the angular variable and a modified version of the finite volume method in the spatial variable. The solution is obtained by an iterative method, and we present a necessary condition for its convergence based on norm operations.

Suggested Citation

  • C. A. Ladeia & H. R. Zanetti & D. L. Gisch & M. Schramm & J. C. L. Fernandes, 2022. "A Simple Numerical Scheme to Obtain Reflectivity and Transmissivity of an Isotropically Scattering Slab," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 169-178, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_12
    DOI: 10.1007/978-3-031-07171-3_12
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-07171-3_12. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.