Heat generation theory

A number of mechanisms have been proposed by which this common irradiated state is obtained. The most widely accepted is the thermal spike theory, which considers the heat generated in the wake of a fast particle passing through a soHd as being sufficient to cause severe stmctural disturbances which are then fro2en in by rapid cooling. Many property changes can be explained by this theory (146). 

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

Critical heat production rates (i.e., heat production rates that still do not lead to a runaway), are often determined by small scale experiments. However, the effect of scale-up on these rates, as discussed in [161], must be taken into account. An indication of the effect of scaling in an unstirred system is shown in Figure 3.2. In this figure, the heat production rate (logarithmic scale) is shown as a function of the reciprocal temperature. Point A in the figure represents critical conditions (equivalent heat generation and heat removal) obtained in a 200 cm3 Dewar vessel set-up. It can be calculated from the Frank-Kamenetskii theory on heat accumulation [157, 162] that the critical conditions are lowered by a factor of about 12 for a 200 liter insulated drum. These conditions are represented by... 

Nineteenth Century Chemistry Caloric Theory and Thermodynamics Lavoisier proposed in the late 18th century that the heat generated by combustion was due to a weightless material substance called caloric that flowed from one place to another and was never destroyed. 

The theory advanced by De Ris belongs to the first group. In his model of flame spread along a horizontal surface it is assumed that the diffusion flame contacts the surface at the point where the polymer vaporization (gasification) begins. Reactant diffusion to the narrow zone of chemical reaction controls the heat generation process. If heat is transferred from the laminar diffusion flame to the surface by conduction, then the flame spread rate follows the Equations a) for thermally thin materials... 

As stated in Preface, the basic concept of the thermal explosion theory is that whether the thermal explosion or the spontaneous ignition of a chemical of the TD type, including every gas-permeable oxidatively-heating substance, having an arbitrary shape and an arbitrary size, placed in the atmosphere under isothermal conditions, occurs or not is decided, based on the balance between the rate of heat generation in the chemical and the rate of heat transfer from the chemical to the atmosphere at the critical state for the thermal explosion which exists at the end of the early stages of the self-heating process. 

The present paper (just as previous ones, references 2-6) considers the thermal mechanism as being responsible for the formation of DSs. In other words, the factor of nonlinearity is here the exponential dependence of the reaction heat generation intensity on temperature, which is the commonest in chemistry, and the concentration-velocity relation corresponds to the linear case of a first-order reaction. Consideration of the chemically simplest case aims at forming a basis of the theory of DS in heterogeneous catalysis and its further development by consistently complicating the kinetic law of a reaction and introducing into the model nonlinearities (feedbacks) of both... 

Instability typically arises from the interaction of two phenomena with different dependences on a reaction parameter In a nonisothermal reaction, the dependence on temperature is exponential for heat generation by the reaction, but linear for heat loss to the cooling coil or environment in a reaction with chain branching, the dependence on radical population is exponential for acceleration by branching, but quadratic for chain termination. A reaction is unstable if acceleration outruns retardation. This can cause an explosion or, in a CSTR, lead to multiple steady states. Feinberg s network theory can help to assess whether an isothermal reaction admits multiple steady states in a CSTR. 

Calculation of Interfacial Temperature by Continuum Heat Conduction Theory A Stochastic Model for Interfacial Temperature Generated at Discrete Sites... 

The hot-spot theory, expounded by Bowden and Yoffe in their earlier work [2], is the foundation for most of their interpretations of initiation experiments. Heat (certainly), shock, friction, and intense electron beams were aU described as causing localized heating, such that if the region grows beyond a critical size the rate of heat generation exceeds the rate of heat loss and explosion occurs. 

The theory of heat generation by mobile dislocations was given by Eshelby and Pratt [73] in terms of the temperature rise AT produced by the movement of n dislocations at a velocity F in a medium of thermal diffusivity a. Two cases were considered, one in which the mean spacing of the dislocations X is much smaller than A = 2a/F, and that for which X A. The final expressions have the form... 

According to this theory, when the temperature is low, practically no reaction occurs within a mixture between the fuel and the oxygen of the air. Active molecules of oxygen necessary for such a reaction to take place are absent unless the mixture is heated first. Only then can the oxidation reaction begin. The amount of heat generated in this process, per unit of time, can be calculated as follows ... 

A significant number of authors have modeled the theory of heat generation and heat dissipation in CE [4,9-13]. The rate of Joule heating (P), which is the resistive heating power that occurs when an electric current (/) flows through the electrolyte, can be quantified simply using the following equation ... 

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