Frank-Kamenetskii parameter

Critical Values of Frank-Kamenetskii Parameter for a Self-heating Slab of Hard Disks (0 = 175)... 

By incorporating small amounts of impurities in expls, such as LA, the thermal parameters of the Frank-Kamenetskii equation hardly change, but the induction periods notably change... 

The parameter 8 is called the form factor or the Frank-Kamenetskii number. When a solution of Equation 13.26 exists, a stationary temperature profile can be established and the situation is stable. When there is no solution, no steady state can be established and the solid enters a runaway situation. The existence, or not, of a solution to the differential Equation 13.26, depends on the value of parameter 8, which therefore is a discriminator. The differential equation can be solved for simple shapes of the solid body, for which the Laplacian can be defined ... 

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

Effects of Reaction Parameters An unusual feature of Equation (15) is that it does not appear to involve the heat of reaction and heat capacity. This is because they were algebraically eliminated by combining the Frank-Kamenetskii relation,... 

The initial conditions are (p = 1 and 6 = 6q (Tq — T )E/(R Ti) at t = 0. The simplest approximation to the function /(cp) is / — cp. Here a is the ratio of a transfer coefficient for fuel to that for heat, 6 is a ratio of the thermal energy at wall temperature to the activation energy (see Section B.3), y is a ratio of the thermal energy at wall temperature to the total energy released by the reaction, and eyS is the ratio of the cooling time to the characteristic time of chemical reaction at the wall temperature. Frank-Kamenetskii [28] has emphasized that in combustion, the parameters e and y are small. He also introduced the parameter 3, defined in equation (55), as occupying a role of central importance in thermal explosions. 

We have to confess that very often such questions are not taken into account and by no means does every experiment meet the minimal requirements for comparison with simula ted data. Vast experience gained in the area of heat- and mass-transfer in combustion (Frank-Kamenetskii, 1969) indicates that the most appropriate for comparison with model calculations are relative parameters and criteria, which are less influenced by the particular experimental hardware and the scale of process. 

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

This set of two equations contains many kinetic, geometric, and thermal parameters. The phase variables of this system are the reactant concentration and the temperature. We can introduce the following dimensionless parameters (Frank-Kamenetskii, 1969) ... 

Equation (46.6) is taken as the departure point in the Zel dovich and Frank-Kamenetskii theory. Provided the condition for the similarity of the temperature and concentration fields is fulfilled, the above expression yields for reactions of various orders the value Uq defined by parameters X, Cp, T, Tq/T, E (E is the effective activation energy). 

Frank-Kamenetskii solved his equation under the steady-state condition dTjdt = 0 and obtained the following expression for critical temperature in terms of the related physical parameters. 

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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