Frank-Kamenetskii number, reaction

The Frank-Kamenetskii number, or parameter 8, characterizing the reaction is... 

Frank-Kamenetskii number for the degree of reaction activation parameters evaluating the ratios of the characteristic thermal and diffusion times and lengths... 

Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

Even though the governing phenomena of coupled reaction and mass transfer in porous media are principally known since the days of Thiele (1) and Frank-Kamenetskii (2), they are still not frequently used in the modeling of complex organic systems, involving sequences of parallel and consecutive reactions. Simple ad hoc methods, such as evaluation of Thiele modulus and Biot number for first-order reactions are not sufficient for such a network comprising slow and rapid steps with non-linear reaction kinetics. 

Sebastian (2,6) following Frank-Kamenetskii (43) arrived at the results depicted on Fig. 11.7, where the Nusselt (Nu) dimensionless number Nu = hRH/k, k is the thermal conductivity, tH is the characteristic time for removing the reaction-generated heat by conduction... 

The Frank-Kamenetskii approximation reduces the analysis to a one-parameter description it is useful for showing that the competition between heat production and heat removal indeed leads to the existence of criticality. However, this approximation ignores another important aspect of chemical kinetics, that of finite reaction activation energy. The effect of nonzero e in f(0) can be analyzed using a number of different approximations [4-6], By writing... 

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