Non-isothermal polymerization in a batch-process reactor

In current industrial practice, reactive processing carried out in non-isothermal conditions, for both inherent and other reasons, such as changes in temperature at the surface of an article during the process cycle. Inherent reasons are the existence of inner heat sources, which can be of chemical origin (enthalpy of reaction), heat of phase transition from crystallization of a newly formed polymer or heat dissipated due to the flow of a reactive mass. 

Transfer of the theoretical results obtained for isothermal conditions to the non-isothermal case is rather simple provided the temperature dependencies of the constants are known. A theoretical analysis of non-isothermal processes may be limited by thermal runaway, which is equivalent to the thermal instability already thoroughly studied for chemical reactors.80,81 There are two limiting situations, known as the Semenov and Frank-Kamenetzky models 80,82 these correspond to periodic ideal stirred and periodic ideal plug reactors, respectively. 

Temperature and concentration gradients are absent inside an ideal stirred reactor. Mixing can be achieved by forced or free-convective movement of a material. For such a reactor the energy balance equation can be written as  

Based on these assumptions, the mathematical formulation for condensed media can be expressed by the following system of equations  

The initial conditions are at t = 0, T = To, andp = 0. The parameter n characterizes the dimensions of the volume for a parallel plate reactor n = 0 for a cylindrical reactor n = 1 and for a spherical reactor n = 2. In these equations, x is a space coordinate A. is the coefficient of thermal conductivity r is the characteristic size of the reactor k is the heat transfer coefficient and To is the initial temperature of the initial medium. 

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