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Heat and Mass Transfer

, Volume 50, Issue 7, pp 1031–1036 | Cite as

Heterogeneous thermochemical decomposition of a semi-transparent particle under high-flux irradiation: uniform versus non-uniform irradiation

  • Pirmin Philipp Ebner
  • Wojciech Lipiński
Technical Note

Abstract

The effects of a semi-transparent reacting particle irradiation are analysed using a transient combined heat transfer model. Direct uniform irradiation is found to be favourable for particle heating and decomposition, decreasing the total reaction time by a factor of 3.3 as compared to that for non-uniform irradiation. In both cases heat transfer from the surface to the reaction zone is the process limiting mechanism.

Keywords

Particle Irradiation CaCO3 Particle Volumetric Heat Source Heat Transfer Mode Heat Transfer Limitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

Area (m−2)

\( \bar{c}_{p} \)

Specific heat at constant pressure (J mol−1 K−1)

Ec

Activation energy of chemical reaction rate constant (J mol−1)

h

Heat transfer coefficient (W m−2 K−1)

\( \bar{h} \)

Specific enthalpy (J mol−1)

Iλ

Spectral radiation intensity (W m−2 μm−1 sr−1)

kc

Chemical reaction rate constant (mol m−2 s−1)

k0

Pre-exponential factor of chemical reaction (mol m−2 s−1)

k

Thermal conductivity (W m−1 K−1)

N

Amount of substance (mol)

n

Refractive index

\( {\hat{\mathbf{n}}} \)

Unit normal vector

p

Pressure (Pa)

\( \dot{q} \)

Heat flux (W m−2)

\( \bar{R} \)

Universal gas constant (8.314 J mol−1 K−1)

r

Radius (m)

\( \bar{r} \)

Reaction rate (mol m−3 s−1)

\( {\hat{\mathbf{k}}} \)

Unit vector into the z-direction

Sv

Volume based specific surface area (m2 m−3)

\( \dot{S} \)

Volumetric heat source (W m−3)

T

Temperature (K)

t

Time (s)

\( \bar{V} \)

Molar volume (m3 mol−1)

V

Volume (m3)

x, y, z

Cartesian coordinates (m)

X

Reaction extent

Greek symbols

β

Extinction coefficient (m−1)

\( \Delta H^{0}_{{ 2 9 8 {\text{K}}}} \)

Standard enthalpy of reaction (J mol−1)

λ

Wavelength (μm)

ν

Stoichiometric coefficient

\( \bar{\rho } \)

Molar concentration (mol m−3)

ρ

Reflectivity

θ

Polar angle (rad)

σ

Stefan–Boltzmann constant (σ = 5.6704 × 10−8 W m−2 K−4)

Subscripts

a

Absorption

b

Blackbody

CaCO3

Calcium carbonate

CaO

Calcium oxide

CO2

Carbon dioxide

chem

Chemical

cond

Conduction

eff

Effective

em

Emission

ext

External

gr

Grain

i

Component index

p

Particle particle surface

rad

Radiative

λ

Spectral

0

Initial

Other symbols

Del operator

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mechanical and Process EngineeringETH ZurichZurichSwitzerland
  2. 2.Research School of EngineeringAustralian National UniversityCanberraAustralia

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