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Mathematical modeling of sulfide flash smelting process: Part II. Quantitative analysis of radiative heat transfer

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Abstract

A mathematical model has been developed to describe the rate processes in an axisymmetric copper flash smelting furnace shaft. A particular feature of the model is the incorporation of the four-flux model to describe the radiative heat transfer by combining the absorbing, emitting, and anisotropic scattering phenomena. The importance of various subprocesses of the radiative heat transfer in a flash smelting furnace has been studied. Model predictions showed that the radiation from the furnace walls and between the particles and the surrounding is the dominant mode of heat transfer in a flash smelting furnace.

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Abbreviations

A :

cross-sectional area of the furnace

b :

backward scattering component, defined in Eq. [13]

C i :

terms defined by Eqs. [23] through [26]

C s :

scattering cross section in Eq. [44]

d :

particle diameter

d1 :

diameter of the single-entry burner

d f :

diameter of the furnace

f :

forward scattering component, defined in Eq. [12]

F:

radiative flux sum vector, Eq. [28]

I :

radiative flux

K :

radiative coefficient

l :

distance coordinate

l m :

mean beam length defined by Eq. [39]

L f :

furnace length

n :

particle number density

p(β) :

phase (or scattering) function occurring in Eq. [1]

P s :

particle size diameter defined by Eq. [42]

q rp :

radiative heat transfer rate for the particle phase

Q:

net radiation flux, Eq. [27]

Q r :

total volumetric radiative heat transfer rate, Eq. [32]

Q rg :

volumetric heat transfer rate by gas-phase radiation, Eq. [34]

r :

radial distance from the centerline

s :

sidewise scattering component, defined in Eq. [14]

T :

temperature

V :

volume of the furnace

W i :

terms defined by Eqs. [8] through [11]

x :

axial distance from the burner exit

β :

scattering angle

Γf :

term defined by Eq. [31]

ε :

emissivity

η a , η s :

absorption and scattering efficiencies of particles, respectively

λ :

wavelength of radiation

ρ :

reflectivity

σ :

Stefan-Boltzmann constant

ω0 :

albedo, defined in Eq. [15]

Ω:

solid angle

a :

absorption

8 :

gas

o :

inlet

s :

scattering

t :

extinction

w :

wall

+:

positive direction on a major axis

-:

negative direction on a major axis

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Authors and Affiliations

  1. Lucky Metals Corporation, Seoul, Korea

    Y. B. Hahn (Research Engineer)

  2. Department of Metallurgical Engineering, University of Utah, 84112-1183, Salt Lake City, UT

    H. Y. Sohn (Professor)

Authors
  1. Y. B. Hahn
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  2. H. Y. Sohn
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Formerly Graduate Student, Department of Metallurgical Engineering, University of Utah.

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Hahn, Y.B., Sohn, H.Y. Mathematical modeling of sulfide flash smelting process: Part II. Quantitative analysis of radiative heat transfer. Metall Trans B 21, 959–966 (1990). https://doi.org/10.1007/BF02670266

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