Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation

Menahem Krief; Ryan G. McClarren

doi:10.13182/mc25-47008

Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation

Menahem Krief^*
, Ryan G. McClarren

^*Corresponding author for this work

Racah Institute of Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Generalized similarity solutions to the nonlinear non-equilibrium Marshak wave problem are de-veloped. The solutions exist for a problem which is specified in terms of various power laws. Specifically, we assume power laws for the time dependent surface temperature, the spatial density profile and as well as material model with power law temperature and density dependent and specific energy density. It is shown that the solutions exist for specific values of the temporal temperature opacities drive and spatial density exponents, which must obey a certain relationship with the material temperature and density exponents. The properties of the solutions are investigated. Finally, we compare the theoretical results with numerical gray diffusion and transport simulations.

Original language	English
Title of host publication	Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025
Publisher	American Nuclear Society
Pages	1538-1546
Number of pages	9
ISBN (Electronic)	9780894482229
DOIs	https://doi.org/10.13182/mc25-47008
State	Published - 2025
Event	2025 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025 - Denver, United States Duration: 27 Apr 2025 → 30 Apr 2025

Publication series

Name	Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025

Conference

Conference	2025 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025
Country/Territory	United States
City	Denver
Period	27/04/25 → 30/04/25

Bibliographical note

Publisher Copyright:
© 2025 AMERICAN NUCLEAR SOCIETY, INCORPORATED, WESTMONT, ILLINOIS 60559

Keywords

Marshak waves
Radiation transport

Access to Document

10.13182/mc25-47008

Cite this

Krief, M., & McClarren, R. G. (2025). Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation. In Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025 (pp. 1538-1546). (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025). American Nuclear Society. https://doi.org/10.13182/mc25-47008

Krief, Menahem ; McClarren, Ryan G. / Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation. Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025. American Nuclear Society, 2025. pp. 1538-1546 (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025).

@inproceedings{3014b1739c1740f68c4ad7a44817d65b,

title = "Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation",

abstract = "Generalized similarity solutions to the nonlinear non-equilibrium Marshak wave problem are de-veloped. The solutions exist for a problem which is specified in terms of various power laws. Specifically, we assume power laws for the time dependent surface temperature, the spatial density profile and as well as material model with power law temperature and density dependent and specific energy density. It is shown that the solutions exist for specific values of the temporal temperature opacities drive and spatial density exponents, which must obey a certain relationship with the material temperature and density exponents. The properties of the solutions are investigated. Finally, we compare the theoretical results with numerical gray diffusion and transport simulations.",

keywords = "Marshak waves, Radiation transport",

author = "Menahem Krief and McClarren, \{Ryan G.\}",

note = "Publisher Copyright: {\textcopyright} 2025 AMERICAN NUCLEAR SOCIETY, INCORPORATED, WESTMONT, ILLINOIS 60559; 2025 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025 ; Conference date: 27-04-2025 Through 30-04-2025",

year = "2025",

doi = "10.13182/mc25-47008",

language = "אנגלית",

series = "Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025",

publisher = "American Nuclear Society",

pages = "1538--1546",

booktitle = "Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025",

address = "ארצות הברית",

}

Krief, M & McClarren, RG 2025, Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation. in Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025. Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025, American Nuclear Society, pp. 1538-1546, 2025 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025, Denver, United States, 27/04/25. https://doi.org/10.13182/mc25-47008

Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation. / Krief, Menahem; McClarren, Ryan G.
Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025. American Nuclear Society, 2025. p. 1538-1546 (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation

AU - Krief, Menahem

AU - McClarren, Ryan G.

PY - 2025

Y1 - 2025

N2 - Generalized similarity solutions to the nonlinear non-equilibrium Marshak wave problem are de-veloped. The solutions exist for a problem which is specified in terms of various power laws. Specifically, we assume power laws for the time dependent surface temperature, the spatial density profile and as well as material model with power law temperature and density dependent and specific energy density. It is shown that the solutions exist for specific values of the temporal temperature opacities drive and spatial density exponents, which must obey a certain relationship with the material temperature and density exponents. The properties of the solutions are investigated. Finally, we compare the theoretical results with numerical gray diffusion and transport simulations.

AB - Generalized similarity solutions to the nonlinear non-equilibrium Marshak wave problem are de-veloped. The solutions exist for a problem which is specified in terms of various power laws. Specifically, we assume power laws for the time dependent surface temperature, the spatial density profile and as well as material model with power law temperature and density dependent and specific energy density. It is shown that the solutions exist for specific values of the temporal temperature opacities drive and spatial density exponents, which must obey a certain relationship with the material temperature and density exponents. The properties of the solutions are investigated. Finally, we compare the theoretical results with numerical gray diffusion and transport simulations.

KW - Marshak waves

KW - Radiation transport

UR - https://www.scopus.com/pages/publications/105010181584

U2 - 10.13182/mc25-47008

DO - 10.13182/mc25-47008

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:105010181584

T3 - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025

SP - 1538

EP - 1546

BT - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025

PB - American Nuclear Society

T2 - 2025 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025

Y2 - 27 April 2025 through 30 April 2025

ER -

Krief M, McClarren RG. Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation. In Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025. American Nuclear Society. 2025. p. 1538-1546. (Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2025). doi: 10.13182/mc25-47008

Generalized non-equilibrium Marshak wave solutions in the gray diffusion approximation

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this