TY - JOUR
T1 - Numerical solution of Rosseland model for transient thermal radiation in non-grey optically thick media using enriched basis functions
AU - Malek, Mustapha
AU - Izem, Nouh
AU - Mohamed, M. Shadi
AU - Seaid, Mohammed
AU - Wakrim, Mohamed
N1 - Funding Information:
Financial support provided by the project of Qatar National Research Fund under the contract NPRP11S-1220-170112 is gratefully acknowledged.
Publisher Copyright:
© 2020 International Association for Mathematics and Computers in Simulation (IMACS)
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2021/2
Y1 - 2021/2
N2 - Heat radiation in optically thick non-grey media can be well approximated with the Rosseland model which is a class of nonlinear diffusion equations with convective boundary conditions. The optical spectrum is divided into a set of finite bands with constant absorption coefficients but with variable Planckian diffusion coefficients. This simplification reduces the computational costs significantly compared to solving a full radiative heat transfer model. Therefore, the model is very popular for industrial and engineering applications. However, the opaque nature of the media often results in thermal boundary layers that requires highly refined meshes, to be recovered numerically. Such meshes can significantly hinder the performance of numerical methods. In this work we explore for the first time using enriched basis functions for the model in order to avoid using refined meshes. In particular, we discuss the finite element method when using basis functions enriched with a combination of exponential and hyperbolic functions. We show that the enrichment can resolve thermal boundary layers on coarse meshes and with few elements. Comparisons to the standard finite element method for thermal radiation in non-grey optically thick media with multi-frequency bands show the efficiency of the approach. Although we mainly study the enriched basis functions in glass cooling applications the substantial saving in the computational requirements makes the approach highly relevant to a large number of engineering applications that involve solving the Rosseland model.
AB - Heat radiation in optically thick non-grey media can be well approximated with the Rosseland model which is a class of nonlinear diffusion equations with convective boundary conditions. The optical spectrum is divided into a set of finite bands with constant absorption coefficients but with variable Planckian diffusion coefficients. This simplification reduces the computational costs significantly compared to solving a full radiative heat transfer model. Therefore, the model is very popular for industrial and engineering applications. However, the opaque nature of the media often results in thermal boundary layers that requires highly refined meshes, to be recovered numerically. Such meshes can significantly hinder the performance of numerical methods. In this work we explore for the first time using enriched basis functions for the model in order to avoid using refined meshes. In particular, we discuss the finite element method when using basis functions enriched with a combination of exponential and hyperbolic functions. We show that the enrichment can resolve thermal boundary layers on coarse meshes and with few elements. Comparisons to the standard finite element method for thermal radiation in non-grey optically thick media with multi-frequency bands show the efficiency of the approach. Although we mainly study the enriched basis functions in glass cooling applications the substantial saving in the computational requirements makes the approach highly relevant to a large number of engineering applications that involve solving the Rosseland model.
KW - Finite element method
KW - Glass cooling
KW - Partition of unity method
KW - Radiative heat transfer
KW - Rosseland model
KW - Thermal boundary layers
UR - http://www.scopus.com/inward/record.url?scp=85090546856&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2020.08.024
DO - 10.1016/j.matcom.2020.08.024
M3 - Article
SN - 0378-4754
VL - 180
SP - 258
EP - 275
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
ER -