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Influence of multi-dimensional oscillating combustion fronts on thermal profiles

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Abstract

A multi-dimensional numerical model for micropyretic/combustion synthesis was developed and then applied to a special configuration. The configuration was chosen to illustrate the differences between one-dimensional and two-dimensional combustion. The features of the model include the melting of each constituent of the reactants and the products, and considerations of porosity for both the reactants and the products. Application of this model to the oscillatory combustion synthesis of TiB2 has been carried out, for the first time, to study two-dimensional-combustion-front movement. The model predicts higher hot-spot temperatures in a two-dimensional situation than those obtained in a one-dimensional experiment. Additionally, hot spots are noted to traverse along orthogonal directions. Some processing implications of such results are examined.

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Abbreviations

APℴ,AP :

Finite-difference coefficients

B :

Breadth of specimen (m)

C PUA :

Specific heat of reactant A at 300K (J kg−1 K−1)

C PUB :

Specific heat of reactant B at 300K (J kg−1 K−1)

C P :

Specific heat of reactants at higher temperatures (J kg−1 K−1)

C PU :

Specific heat of unreacted Reactants A and B at 300K(J kg−1 K−1)

E :

Activation Energy (J mol−1)

H :

Enthalpy (J kg−1)

K :

Dimensionless thermal conductivity

K U :

Thermal conductivity of the reactants A, B at 300K(W m−1K−1)

K 0 :

Frequency factor (s−1)

δH SLA :

Latent heat release at the melting point of Reactant A (J kg−1)

n :

New time level

o :

Old time level

m :

Iteration number

K * :

Thermal conductivity of A, B and AB in the reaction zone (W mK−1)

L :

Length of specimen (m)

M :

Melting parameter

Q :

Heat of reaction (J kg−1)

R :

Universal gas constant (J mol−1 K−1)

t :

Time (s)

T :

Temperature (K)

T C :

Combustion temperature (K)

T 0 :

Ambient temperature (K)

X, Y :

Dimensionless co-ordinates

X *,Y * :

Co-ordinates (m)

ρ:

Density of reactants at 300 K (kg m−3)

Ø:

Dimensionless enthalpy

θ:

Dimensionless temperature

Τ:

Dimensionless time

η:

Dimensionless fraction of reacted product

n :

Northern side of control volume

N :

Northern control volume

P :

Centre of current control volume

s :

Southern side of control volume

S :

Southern control volume

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Authors and Affiliations

  1. International Center for Micropyretics and Department of Materials Science and Engineering, University of Cincinnati, 45221, Cincinnati, OH, USA

    M. G. Lakshmikantha & J. A. Sekhar

Authors
  1. M. G. Lakshmikantha
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  2. J. A. Sekhar
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Lakshmikantha, M.G., Sekhar, J.A. Influence of multi-dimensional oscillating combustion fronts on thermal profiles. J Mater Sci 28, 6403–6408 (1993). https://doi.org/10.1007/BF01352204

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  • DOI: https://doi.org/10.1007/BF01352204

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