Abstract
Heat radiation in gases or plasmas is usually out of local thermodynamic equilibrium (LTE) even if the underlying matter is in LTE. Radiative transfer can then be described with the radiative transfer equation (RTE) for the radiation intensity. A common approach to solve the RTE consists in a moment expansion of the radiation intensity, which leads to an infinite set of coupled hyperbolic partial differential equations for the moments. A truncation of the moment equations requires the definition of a closure. We recommend to use a closure based on a constrained minimum entropy production rate principle. It yields transport coefficients (e.g., effective mean absorption coefficients and Eddington factor) in accordance with the analytically known limit cases. In particular, it corrects errors and drawbacks from other closures often used, like the maximum entropy principle (e.g., the M1 approximation) and the isotropic diffusive P1 approximation. This chapter provides a theoretical overview on the entropy production closure, with results for an illustrative artificial example and for a realistic air plasma.
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Notes
- 1.
In the following we will skip the term specific.
- 2.
Three and more photon processes are disregarded.
References
Chandrasekhar, S.: Radiative Transfer. Dover Publ. Inc, New York (1960)
Jones, G.R., Fang, M.T.C.: The physics of high-power arcs. Rep. Prog. Phys. 43, 1415 (1980)
Siegel, R., Howell, J.R.: Thermal Radiation Heat Transfer. Washington, Philadelphia (1992)
Landau, L.D., Lifshitz, E.M.: Statistical Physics. Elsevier, Amsterdam (2005)
Tien, C.L,: Radiation properties of gases. In: Irvine Jr, T.F, Hartnett, J.P (eds.) Advances in heat transfer, vol. 5. Academic Press, Inc., New York, 253 (1968)
Chen, G.: Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons. Oxford University Press, USA (2005)
Christen, T., Kassubek, F.: Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer. J. Quant. Spectrosc. Radiat. Transfer. 110, 452 (2009)
Christen T, Kassubek F, and Gati R.: Radiative heat transfer and effective transport coefficients. In: Aziz Belmiloudi (ed.) Heat Transfer—Mathematical modelling, numerical methods and information technology, InTech, Rijeka, Croatia (2011)
Kohler, M.: Behandlung von Nichtgleichgewichtsvorg¨angen mit Hilfe eines Extremalprinips. Z. Physik 124, 772 (1948)
Ziman, J.M.: The general variational principle of transport theory. Can. J. Phys. 34, 1256 (1956)
Ziman, J.M.: Electrons and Phonons. Clarendon Press, Oxford (1967)
Martyushev, L.M., Seleznev, V.D.: Maximum entropy production principle in physics, chemistry, and biology. Phys. Rep. 426, 1 (2006)
Minerbo, G.N.: Maximum entropy Eddington factors. J. Quant. Spectrosc. Radiat. Transfer. 20, 541 (1978)
Levermore, C.D.: Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83, 1021 (1996)
Turpault, R.: A consistent multigroup model for radiative transfer and its underlying mean opacities. J. Quant. Spectrosc. Radiat. Transfer. 94, 357 (2005)
Essex, C.: Minimum entropy production in the steady state and radiative transfer. The Astrophys. J. 285, 279 (1984)
Würfel, P., Ruppel, W.: The flow equilibrium of a body in a radiative field. J. Phys. C: Solid State Phys. 18, 2987 (1985)
Kabelac, S.: Thermodynamik der Strahlung. Vieweg, Braunschweig (1994)
Santillan, M., de Parga, G.A., Angulo-Brown, F.: Black-body radiation and the maximum entropy production regime. Eur. J. Phys. 19, 361 (1998)
Christen, T.: Nonequilibrium distribution function and generalized hydrodynamics for independent electrons from an entropy production rate principle. Europhys. Lett. 89, 57007 (2010)
Oxenius, J.: Radiative transfer and irreversibility. J. Quant. Spectrosc. Radiat. Transfer 6, 65 (1966)
Kröll, W.: Properties of the entropy production due to radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 7, 715 (1967)
Struchtrup H.: Rational extended thermodynamics Müller I and Ruggeri T. (ed.) p. 308. Springer, New York, Second Edition (1998)
Christen, T.: Modeling electric discharges with entropy production rate principles. Entropy 11, 1042 (2009)
Kershaw D, Flux limiters nature’s own way Lawrence Livermore Laboratory UCRL-78378 (1976)
Nordborg, H., Iordanidis, A.: Self-consistent radiation based modelling of electric arcs: I. Efficient radiation approximations. J. Phys. D Appl. Phys. 41, 135205 (2008)
Essex C and Kennedy DC J. Stat. Phys. 94, 253 (1999). (or Minimum entropy production of neutrino radiation in the steady state, Report No: DOE/ER/40272-280 UFIFT-HEP-97- 7)
Data for the air spectrum has been provided by R. Gati (ABB Corporate Research) with use of tools by V. Aubrecht
Aubrecht, V., Lowke, J.J.: Calculations of radiation transfer in SF6 plasmas using the method of partial characteristics. J. Phys. D Appl. Phys. 27, 2066 (1994)
Chaveau, S., et al.: Radiative transfer in LTE air plasmas for temperatures up to 15,000 K. J. Quant. Spectrosc. Radiat. Transfer. 77, 113 (2003)
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Christen, T., Kassubek, F. (2014). Entropy Production-Based Closure of the Moment Equations for Radiative Transfer. In: Dewar, R., Lineweaver, C., Niven, R., Regenauer-Lieb, K. (eds) Beyond the Second Law. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40154-1_12
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