Burning rate - an eigenvalue

There is only one value of m - an eigenvalue - that will satisfy a given set of environmental and fuel property conditions. How can this be found We must be creative. We have already pushed the chemical kinetic terms out of the problem, but surely they must not have disappeared in reality. 

Let us recall from the discussion of liquid evaporation that thermodynamically we have a property relationship between fuel vapor concentration and surface temperature, 

If we know b(0), we have our answer, but we have several alternatives for b bFj. b y[ or b0F. Any of these is fine. We chose bQ[ because it gives us the most expedient approximate answer  

We do expect Y0l (0) to be zero at the surface for combustion within the boundary layer since the flame reaction is fast and no oxygen is left. This must be clearly true even if the chemistry is not so fast. Moreover, since we are heating the surface with a nearby flame that approaches an adiabatic flame temperature, we would expect a high surface temperature. For a liquid fuel, we must have 

The dimensionless group in the log term is called the Spalding B number, named after Professor Brian D. Spalding who demonstrated its early use [5], From Equation (9.39), the surface conditions give 

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