Heat Transfer at the Burning Surface

Referring to Eq. (3.49), the temperature gradient in the fizz zone, represented by is given by the heat balance at the burning surface  

Since cjijand r of the catalyzed propellant are pressure-independent in the plateau region and Qf is nearly constant, oiy should also be pressure-independent. This is a significant difference when compared with commonly observed bimolecular gas-phase reactions. Referring to Eq. (3.33), the reaction rate in the gas phase, oig, is given as a function of pressure according to 

The effective overall order of the fizz zone reaction, k, is determined to be zero for plateau burning, and approximately 1.4for super-rate burning. The reaction order for the non-catalyzed propellant is also determined to be approximately 1.7, that is, nearly equal to the order of a conventional gas-phase reaction. 

1 Kubota, N., and Masamoto, T., Flame Structures and Burning Rate Characteristics of CMDB Propellants, 16th Symposium (International) on Combustion, The Combustion Instimte, Pittsburgh, PA, 1976, pp. 1201-1209. 

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