III International Conference

PP-III-89of entropy in a system provide deeper insight in the physical nature of these complexnonlinear phenomena. The variational principles of the thermodynamics of irreversibleprocesses were extended to slow heat autowaves, which arose in a bed of a preliminary heatedcatalyst when a cold reaction mixture was supplied [1]. When a reversible reaction occurred,fast heat autowaves could propagate alongside well-known slow heat autowaves. Theexistence of such autowaves became known only after theoretical studies. The existence of aspatial-temporal dissipative structure (a fast heat autowave) near the thermodynamicallyequilibrium state was established.The development of new technological processes on basis of autowave phenomenasupposes research of influence of every essential factor that characterizes a static catalyst bed[2, 3]. Some of these factors are processes of particle-to-fluid heat and mass transfer in staticcatalyst bed. The mathematical model of autowave processes has been built. This modelincludes the heat and mass transfer coefficients that are determined by given parametervalues. Qualitative and numerical analysis of behavior integral curves of the dynamic systemwith three-dimensional phase space was performed. The peculiarities of topological structureof the dynamic system have been shown, including the draw into singular point twodimensionalinvariant multiplicity mathematically equal autowave solutions. New effectivemethod of searching physically meaningful autowave solution is developed basing onqualitative peculiarities. This method consists of solution of variation problem, every step ofwhich unknown parameter value is calculated – propagation velocity of autowave – andCauchy problem with initial conditions is solved. The cycle of numerical researches iscompleted for some typical collection of parameter values of dynamic system. A number ofregularities are discovered. Discovered regularities show theoretical possibility and variousways of autowave processes stabilization.The work was supported by the Russian Foundation for Basic Research (grants 94-03-08205, 00-03-32465, 05-03-32798).References1. Gerasev A.P. Physics-Uspekhi 74 (10) 991-1016 (2004).2. Gerasev A.P. Combust. Explosion Shock Waves 43 (2) (2007).3. Gerasev A.P. Theor. Found. Chem. Eng. 42 (2) (2007).638