Objectives of mathematical modelling

It is clear that this method cannot be based on the use of similarity parameters since reactive molding in common with other chemical engineering processes, involves nonlinear phenomena that result in the invalidity of similarity conditions as geometric, chemical, and thermal parameters. 

A universal method of handling the problem is mathematical modelling, i.e., a quantitative description by means of a set of equations of the whole complex of interrelated chemical, physical, fluiddynamic, and thermal processes taking place concurrently or consecutively in a reactor. Constants of these equations are determined in laboratory experiments. If the range of determining factors (reactive mass compositions, temperature, reaction rates, and so on) in an actual process lie within or only slightly outside the limits studied in laboratory experiments, the solution of the determining set of equations provides a reliable idea of the process operation. 

This approach, taken to its logical conclusion, makes it possible to achieve two main goals first, to optimize the process so as to provide the maximum possible throughput at minimum cost, and, second, to ensure the required quality level of the final products. Development of a deterministic mathematical model of a process requires an adequate representation of its main constituent stages. This always involves an internal contradiction on the one hand, it is desirable to describe all 

For stage VI, the analysis of inherent (or residual) stresses resulting from nonuniform cooling and heat treatment of final articles appears to be critical.Thus, stages IV to VI should be the subject of mathematical modelling specific to reactive processing (chemical molding processes). 

It should be emphasized that in all these cases, combined or superimposed phenomena must be dealt with, viz. for stage IV, fluiddynamics, kinetics of polymerization, and rheokinetic changes caused by chemical reactions for stage V, polymerization kinetics, crystallization kinetics and heat transfer effects a thermomechanical problem in combination with crystallization kinetics. Construction of a mathematical model requires simultaneous solution of a set of equations in order to describe these related phenomena. 

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