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Two-flux model applied to combined conduction-radiation in a gray planar medium

Zweistrommodell angewandt auf kombinierte Wärmeleitung und -Strahlung in ebenem grauen Medium

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Abstract

A numerical study is made of the thermal characteristics of gases exposed to simultaneous conduction and radiation between parallel plates. Through the use of a gray gas model and the two-flux method, specialized equations are developed that generate a system of nonlinear ordinary differential equations. To facilitate the solution of this system, an iterative strategy is adopted. In order to demonstrate the versatility and accuracy of the proposed methodology, the results of several numerical experiments are presented and compared with benchmark solutions.

Zusammenfassung

Es wurde eine Studie über die thermischen Verhältnisse in einem Gas durchgeführt, das gleichzeitig der Wärmeleitung und der Wärmestrahlung zwischen zwei parallelen Platten ausgesetzt ist. Unter Benutzung eines Modelies für graues Gas und der Zweistrommethode wurden spezielle Korrelationen entwickelt, die ein System nichtlinearer gewöhnlicher Differentialgleichungen darstellen. Zur Erleichterung der Lösung des Gleichungssystems wurde eine spezielle iterative Methode angewandt. Zur Demonstration der Vielseitigkeit und Genauigkeit der vorgeschlagenen Methode wurden Ergebnisse verschiedener numerischer Untersuchungen mit den so erhaltenen Lösungen verglichen.

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Abbreviations

A :

constant, Eq. (5)

G :

total intensity of radiation [W/m2]

¯ G :

dimensionless total intensity of radiation

I :

intensity of radiation [W/m2 str]

k :

thermal conductivity [W/m ‡K]

L :

layer thickness [m]

N :

conduction-radiation parameter=k x a /4 σ T 31

q :

total heat flux [W/m2]

Q t :

dimensionless total heat flow

T :

temperature [‡K]

y :

coordinate [m]

ɛ :

surface emissivity

η :

dimensionless coordinate=y/L

θ :

dimensionless temperature=T/T1

x a :

absorption coefficient [1/m]

σ :

Stefan-Boltzmann constant [W/m2 ‡K4]

Τ :

optical depth=x a y

Τ0 :

optical thickness of the medium=x a L

1:

high temperature plate

2:

low temperature plate

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Authors and Affiliations

  1. Depto. de Termodinamica, Universidad Simon Bolivar, Caracas, Venezuela

    A. Campo & A. Tremante

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  1. A. Campo
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  2. A. Tremante
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Campo, A., Tremante, A. Two-flux model applied to combined conduction-radiation in a gray planar medium. Wärme- und Stoffübertragung 21, 221–225 (1987). https://doi.org/10.1007/BF01004024

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  • DOI: https://doi.org/10.1007/BF01004024

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