Zelenskyi K. Mathematical modeling of nonlinear polymer media in extruders

This problem is especially relevant for processes with distributed parameters, the mathematical models of which are described by partial differential equations with corresponding additional conditions at the boundary of the domain. In recent decades, much attention has been paid to objects with distributed parameters. This is due to the desire to increase the efficiency of mathematical modeling of the dynamics of such objects and processes and the development of automatic and automated control systems, as it is well known that all physical processes and objects are essentially objects with distributed parameters. But the vast majority of models describing the dynamics of objects with distributed parameters are linear models, although it is well known that real physical processes are inherently nonlinear. The methods of mathematical and computer modeling of polymers developed in the dissertation work taking into account nonlinear properties gave the chance to essentially improve quality of modeling, to develop recommendations on designing and improvement of technological processes on manufacturing of cables on ultrahigh voltages. The scientific novelty of the work is that for the first time a method of numerical-analytical solution of nonlinear differential equations in partial derivatives of parabolic type and its application to solve problems of heating the extruder body, heating the polymer mixture in the loading zone, melting zone and homogenizing and crystallizing the polymer melt in the dosing zone. The performed researches give the chance to calculate the optimum sizes of the specified zones at designing of the extrusion equipment intended for production of a wide range of production with use of extrusion devices.