Semenov problem

As in the solution to the simpler Semenov problem (see section 4.3), we expect that as 8 increases (increasing the exothermiscity over the material s ability to lose heat) a critical 8C is reached. At this point, an unsteady solution must hold and we have no valid solution to Equation (5.11). For a given geometric shape of the solid and a given heating condition, there will be a unique <5C that allows this ignition event to occur. For the slab problem described, we see that since Bi is an independent parameter, then Sc must be a function of Bi. 

N. N. Semenov, Problems in Chemical Kinetics and Reactivity, vols. I and II translated by M. Boudart, Princeton University Press, Princeton, N.J., 1958. Provides large reservoirs of information on theories of kinetics and experimental data. 

Suitable criteria, mostly originated in the context of thermal explosion theory [cf. Semenov (1928) Zeldovich et al. (1985)], have been adopted in chemical reactor theory to identify the nature of reactor behavior. These are based on a definition of runaway in mathematical terms which allows us to identify in the reactor parameter space the boundary separating runaway and nonrunaway operating conditions. Most of these criteria are based on some geometrical characteristic of the temperature profile in the system. In particular, in the context of thermal explosion (cf. the batch system considered in the classical Semenov problem) we refer to the temperature profile in time, while in the case of tubular reactors we refer to the temperature profile along the reactor axis. 

N. N. Semenov, Some Problems in Chemical Kinetics and Reactivity, Pergmiion Press, London, 1959. 

Comprehensive discussions on reactor stability theories and safe engineering problems were presented by Eigenberger and Schuler (1986, 1989), Zaldivar (1991), Barton and Rogers (1993), and Grewer (1994). The very basic theory developed by Semenov (1928) for zero-order reactions is very illustrative for a physical explanation of explosion phenomena. The theory enables evaluation of conditions at which thermal explosion will occur. 

Semenov, N. N., Some Problems in Chemical Kinetics and Reactivity (M. Boudart, transl.), Vol. I, p. 19. Princeton Univ. Press, Princeton, New Jersey, 1958. 

The problem of competition of the molecular reaction (direct route) and chain reaction (complicated, multistage route) was firstly considered in the monograph by Semenov [1], The new aspect of this problem appeared recently because the quantum chemistry formulated the rule of conservation of orbital symmetry in chemical and photochemical reactions (Woodward-Hofmann rule [4]). Very often the structure of initial reactants suggests their direct interaction to form the same final products, which are also obtained in the chain reaction, and the thermodynamics does not forbid the reaction with AG < 0. However, the experiment often shows that many reactions of this type occur in a complicated manner through several intermediate stages. For example, the reaction... 

NN Semenov. Some Problems of Chemical Kinetics and Reactivity, vols 1 and 2. London Perga-mon Press, 1958-1959. 

Thus, the variable defined in Eq. (4.35) can be used to develop a new equation in the same manner as Eq. (4.30), and the problem reduces to the solution of only one differential equation. Indeed, either Eq. (4.30) or (4.31) can be solved however, Semenov chose to work with the energy equation. 

While Gray Yang are not denying the usefulness of such ideas, they consider that too literal an application on the distinction can lead to difficulties. For this reason they tried to unify both theories and this problem is discussed in their paper. They also examined the effect of fuel consumption on thermal explosions, definition of critical conditions and the effects of vessel shapes. Finally, the relationship between thermal explosion criteria and flame theoty described by Belles (Ref 2), as well as detonability limits were pointed out. Comments on the paper of Gray Yang of Profs R.R. Baldwin R. Ben-Aim are given on p 1061 of Ref 3 Refs 1) N.N. Semenov, "Chemical Kinetics... 

Semenov (S6) considered generally the effects of a gas drag at the film interface for all the cases listed above for smooth laminar film flow (see Section III, F, 2), and later experimental work confirmed these results (K20, K10, S7) for the case when the film thickness is very small, with no waves present on the film surface, and at moderate gas flow rates. The early treatment by Nusselt (N6, N7) also gave results in agreement with the experimental data obtained under these restricted conditions. Brauer s treatment of the problem (Section III, F, 2) (Bl8) also assumed laminar flow of the film and absence of surface waves. The experimental work of Feind (F2), which refers to countercurrent gas/film flow in a vertical tube, showed that, although such a treatment was useful in predicting the qualitative effects of the gas stream on the film thickness and other properties, the Reynolds number range in which it applied strictly was very limited. 

SEMENOV, NIKOLAI N. (1896-1986). A Russian chemist and physicist who won the Nobel Prize in 1956. He authored books on the chain reaction and problems of chemical kinetics and reactivity, as well as many articles. His work concerning thermal combustion and explosion is utilized in rockets and jet engines. He received his doctorate at Leningrad State University. 

A special place among kinetic studies in combustion is occupied by work on nitrogen oxidation. Begun at the AS USSR Institute of Chemical Physics in the mid-thirties on the initiative of N. N. Semenov, research to determine the feasibility of fixation of atmospheric nitrogen for the production of mineral fertilizers has today found application in the development of environmental protection measures for toxic components of combustion products, including nitrogen oxide. In December, 1939, Ya.B. defended his doctoral dissertation on The Oxidation of Nitrogen in Combustion and Explosions. It was precisely these studies, in which D. A. Frank-Kamenetskii, P. Ya. Sadovnikov, A. A. Rudoy, A. A. Kovalskii, and others actively participated, that led Ya.B. to the problems of combustion and detonation. 

Application of Helfand s theory has been limited due to the necessity for numerical analysis (although FORTRAN code to facilitate calculations is provided by Helfand and Wasserman (1982) ).This problem was circumvented with the introduction of the seminal analytical SSL theory by Semenov (1985). 

---