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'''Magnussen model''' is a popular method for computing reaction rates as a function of both mean concentrations and [[turbulence]] levels (Magnussen and Hjertager).<ref name="Magnussen1976">
{{cite journal 
|author1=Magnussen, B. F. |author2=B. H. Hjertager 
 |name-list-style=amp |title=On Mathematical Models of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion 
|journal = Symposium (International) on Combustion
|volume=16
|issue=1
|year=1977 
|pages=719–729  
|doi=10.1016/S0082-0784(77)80366-4
}}</ref> Originally developed for [[combustion]], it can also be used for liquid reactions by tuning some of its parameters. The model consists of rates calculated by two primary means. An [[Arrhenius equation|Arrhenius]], or kinetic rate, <math>R_{K\_i',k}</math>, for species <math>i'</math> in reaction <math>k</math>, is governed by the local mean species concentrations and temperature in the following way:

:<math>
  R_{K\_i',k} = - \nu_{i',k} M_i A_k T^{\beta_k} \exp{\left( -\frac{E_k}{RT} \right)} \prod_{j'=1}^{N} \left[ C_{j'} \right]^{\eta_{j',k}} = K_{i',k}  M_{i'} \prod_{j'=1}^{N} \left[ C_{j'} \right]^{\eta_{j',k}}
</math>

This expression describes the rate at which species <math>i'</math> is consumed in reaction <math>k</math>. The constants <math>A_k</math> and <math>E_k</math>, the Arrhenius pre-exponential factor and activation energy,
respectively, are adjusted for specific reactions, often as the result of experimental measurements. The stoichiometry for species <math>i'</math> in reaction <math>k</math> is represented by the factor <math>\nu_{i',k}</math>, and is positive or negative, depending upon whether the species serves as a product or reactant. The molecular weight of the species <math>i'</math> appears as the factor <math>M_{i'}</math>. The temperature, <math>T</math>, appears in the exponential term and also as a factor in the rate expression, with an optional exponent, <math>\beta_k</math>. Concentrations of other species, <math>j'</math>, involved in the reaction, <math>\left[ C_{j'} \right]</math>, appear as factors with optional exponents associated with each. Other factors and terms not appearing in the equation, can be added to include effects such as the presence of non-reacting
species in the rate equation. Such so-called third-body reactions are typical of the effect of a catalyst on a reaction, for example. Many of the factors are often collected into a single rate constant, <math>K_{i',k}</math>.

== References ==
{{Reflist}}

{{Reaction mechanisms}}
{{Chemical engg}}

Magnussen, B. F., and B. H. Hjertager, “On Mathematical Mod-
els of Turbulent Combustion with Special Emphasis on Soot For-
mation and Combustion,” Proc. 16th Int. Symp. on Combustion,
The Combustion Institute, Pittsburgh, PA (1976).

[[Category:Chemical kinetics|Chemical engineer]]


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