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Different scenarios in a controlled tubular reactor with a countercurrent coolant. (English) Zbl 0801.35140
Summary: A system of three partial differential equations, representing the dynamics of a tubular reactor with axial diffusion refrigerated by means of a countercurrent fluid, is studied. The PDE system is reduced to an ODE one applying the usual finite differences scheme. The use of a semi- implicit Runge-Kutta method, that has proved itself the most reliable integrator for highly oscillating systems, requires a careful analysis of the numerical integration procedure in order to save computational time. Simulation results show the possibility of chaotic behaviour in a specific parameters range. The variable temperature coolant system does not alter the features of the simplified model with a constant coolant temperature. However, beside the usual period doubling cascade, a mechanism of chaotic transition through type III intermittency and a hysteresis phenomenon are observed. After a preliminary characterization of the chaotic regime by means of the known methods, the paper focuses on the analysis of the new types of scenario.

35Q80 Applications of PDE in areas other than physics (MSC2000)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
92E20 Classical flows, reactions, etc. in chemistry
Full Text: DOI
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