For finite rate chemistry, the reaction rate can easily be calculated. However, the mixture fraction theory simplifies a combustion reaction into a mixing phenomenon, and the difficulties associated with closing non-linear mean reaction rates are avoided.
DearShyamal,
In this case reaction rate is assumed to infinite in a very thin zone. if you plot reaction rate in mixture fraction coordinate, you will get a dirac Delta function.
Here is my understanding of non-premixed flames and their modelling. The most simplest configuration to study non-premixed flame is one dimensional counterflow configuration. Now to establish a non-premixed flame across we supply fuel from one side and oxidizer on other. Now for a particular fuel- oxidizer combinations their are two extreme solution available. (1) equilibrium solution (2) cold flow solution.
Strain rate is one of characteristic of non-premixed flame. At low strain rate the solution is very close to equillibrium and reaction time is very small in comparison to mixing time. In this case we can assume reaction rate to be dirac Delta function and the fuel consumption rate can be assumed to fully mixing controlled. As we start increasing the strain rate ( or start increasing the relative fuel-oxidizer velocity) due to heat loss reaction time decrease and we can no longer assume equilibrium condition. For these case, we use an approach of flamelet modelling, that is we solve all these reaction in 1D at different strain rate values and develop a flamelet like library. Now this library is used as patched solution on flow feild solved for the real problem.
Have a look on this link.
https://www.researchgate.net/publication/322164934_On_extinction_Strain_rate_of_Counterflow_diffusion_flames
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