On a Parametrization for the Layer Thickness Depending on the Transmissivity in a Radiative Transfer Problem

C. A. Ladeia (), A. B. Guimarães (), M. Schramm () and B. E. J. Bodmann ()
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C. A. Ladeia: Math Department of Federal University of Rio Grande do Sul
A. B. Guimarães: Institute of Physics of Federal University of Rio Grande do Sul
M. Schramm: Engineering Center of Federal University of Pelotas
B. E. J. Bodmann: Mechanical Engineering Departament of Federal University of Rio Grande do Sul

Chapter Chapter 14 in Integral Methods in Science and Engineering, 2026, pp 199-210 from Springer

Abstract: Abstract We consider the radiative transfer equation in Cartesian geometry in a one-dimensional heterogeneous participant medium with two layers. The numerical solutions to the linear problem is discussed and obtained by a combination of the discrete ordinates and the finite difference methods. The objective of this work is to show a simple parametric formula for the thickness of one of the layers for a specified transmissivity. Further, we present error estimates for the considered steady-state transport equations with azimuthal symmetry and isotropic scattering.

Date: 2026
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DOI: 10.1007/978-3-032-04458-7_14

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