Solution to radiative transfer equation in a 3-D rectangular enclosure due to discontinuous heat flow divergence Article

First Online: 16 November 2012 Received: 19 June 2012 Accepted: 25 October 2012 DOI :
10.1007/s11012-012-9656-9

Cite this article as: Aghanajafi, C. & Abjadpour, A. Meccanica (2013) 48: 1127. doi:10.1007/s11012-012-9656-9
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Abstract In this paper a new model and computer code is presented by considering singular and discontinuous heat flow divergence. A hybrid model including Smith’s WSGG model and Coppale and Vervish’s model is used for calculating gas radiative properties. Energy equation is solved simultaneously to reach temperature field which specify gas radiative properties. S _{8} order of discrete ordinate method is used to solve RTE. It is assumed that walls of enclosure are gray, diffuse and opaque with specified temperature. Boundary conditions are corrected in each iteration that change temperature field.

Keywords Radiation Discrete ordinate method Gray gas Discontinuous heat flow divergence Nomenclature a _{ε,ν} Emissivity weighting factor for band ν

a _{α,ν} Absorptivity weighting factor for band ν

A _{x,y,z} Area of the control volume in x ,y ,z direction respectively

b _{ε,ν,j} Emissivity polynomial coefficient for band ν

c _{α,ν,j,k} Absorptivity polynomial coefficient

f Interpolation factor for inlet and outlet intensity in the control volume

I Radiation intensity

f _{v} Soot concentration

k _{ν} Absorbance coefficient for band ν

L Characteristic length of enclosure

N _{g} Number of gray gas considered in WSGG

P Total pressure of absorbing emitting gases

Q Heat generated within the medium

T Temperature

Greek symbols α _{g} Gas absorbtivity coefficient

β Extinction coefficient

ε _{g} Gas emissivity coefficient

η Direction cosine for in y direction

μ Direction cosine in x direction

ξ Direction cosine in z direction

ρ _{p} Particle density

σ _{s} Scattering coefficient

Φ _{mj} Scattering phase function

ψ Fraction of self-absorbed heat

ω Scattering albedo

ω _{j} Weight coefficient of direction j

Ω Spherical angle

Subscripts b Black body

e Outlet

g Gas

i Inlet

m m th direction

p Particle

s Surface

Abbreviations DOM discrete ordinate method

FVM finite volume method

SNB statistical narrow band (model)

WSGG weighted sum of gray gases

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Authors and Affiliations 1. Department of Mechanical Engineering K.N. Toosi University of Technology Tehran Iran