brewnog said:
But, if you insist... They're not equations...
No equations?
There are several people who spend and have spent the rest of their lives trying to solve THE equations. Today, they remain as a mystery of science. Combustion equations are the generalization of Navier Stokes equations with reactive flow. Besides such equations are strongly nonlinear, the reactive terms usually attaches an Arrhenius factor which make N-S equations to be more non-linear.
A simple example of how a laminar diffusion flame works mathematically, can be found here:
\frac{\partial \rho u}{\partial x} +\frac{\partial \rho v}{\partial y}=0
\frac{\partial}{\partial x} (\rho u^2+E_{u}P}) +\frac{\partial}{\partial y}\Big( \rho uv-\rho \frac{\partial u}{\partial y}\Big)=0
\frac{\partial \rho uY_{O}}{\partial x} +\frac{\partial}{\partial y}\Big( (\rho vY_{O}-\frac{\rho \partial Y_{O}}{PrLe\partial y}\Big)=\frac{DaS}{1+S} Y_{O} Y_{F} exp(-\frac{\beta}{T})
\frac{\partial \rho uY_{F}}{\partial x} +\frac{\partial}{\partial y}\Big( \rho vY_{F}-\frac{\rho \partial Y_{F}}{PrLe \partial y}\Big)=\frac{Da}{1+S} Y_{O} Y_{F} exp(-\frac{\beta}{T})
\frac{\partial \rho uT}{\partial x} +\frac{\partial}{\partial y} \Big(\rho vT-\frac{\rho \partial T}{Pr \partial y}}\Big)=Da T'Y_{O} Y_{F} exp(-\frac{\beta}{T})
That's only a model (which has been simplified using boundary layer approximation and steady flow) of a diffusion flame of Oxygen and Fuel. As you can see, the equations are coupled and the fluid field is very complex. The equations are written into non dimensional form, as a function of non-dimensional parameters which are famous Numbers: Euler, Damkhöler, Prandtl and Lewis. The reactive term is on the right side, and as you can observe it depends on the reaction chemical kinetics.
Although it can be extracted analytical conclusion of this combustion system using a Burke-Schummann analysis, a numerical computation is needed almost every time you formulate something like this. Theoretician physics and engineers are searching for analytical solutions of this kind of complex fluid flows, and a lot of papers are published every year about that. It is a field of research which is only in its early stages.
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