Meccanica

, Volume 48, Issue 5, pp 1127–1138

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

Article

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. S8 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

aε,ν

Emissivity weighting factor for band ν

aα,ν

Absorptivity weighting factor for band ν

Ax,y,z

Area of the control volume in x,y,z direction respectively

bε,ν,j

Emissivity polynomial coefficient for band ν

cα,ν,j,k

Absorptivity polynomial coefficient

f

Interpolation factor for inlet and outlet intensity in the control volume

I

Radiation intensity

fv

Soot concentration

kν

Absorbance coefficient for band ν

L

Characteristic length of enclosure

Ng

Number of gray gas considered in WSGG

P

Total pressure of absorbing emitting gases

Q

Heat generated within the medium

T

Temperature

Greek symbols

αg

Gas absorbtivity coefficient

β

Extinction coefficient

εg

Gas emissivity coefficient

η

Direction cosine for in y direction

μ

Direction cosine in x direction

ξ

Direction cosine in z direction

ρp

Particle density

σs

Scattering coefficient

Φmj

Scattering phase function

ψ

Fraction of self-absorbed heat

ω

Scattering albedo

ωj

Weight coefficient of direction j

Ω

Spherical angle

Subscripts

b

Black body

e

Outlet

g

Gas

i

Inlet

m

mth 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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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringK.N. Toosi University of TechnologyTehranIran

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