Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous...Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.展开更多
It is very important for reactor design and control to choose and control the temperature throughout the reaction process.The linear stability analysis showed that control parameters contained in a nonlinear kinetic s...It is very important for reactor design and control to choose and control the temperature throughout the reaction process.The linear stability analysis showed that control parameters contained in a nonlinear kinetic system of equations resulted in the diversity of temperature self-organization structures and occurring critical values in Lindemann uni-molecular chemical reaction-diffusion-heat conduction systems.The results of numerical simulations also showed that the differences of occurring critical values of Turing bifurcation led to multiple wave number values of spatially periodic structures of temperature field.Without doubt,these significant results should be considered in order to reasonably design,correctly choose the reactor type and optimally control chemical reactors.展开更多
文摘Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.
文摘It is very important for reactor design and control to choose and control the temperature throughout the reaction process.The linear stability analysis showed that control parameters contained in a nonlinear kinetic system of equations resulted in the diversity of temperature self-organization structures and occurring critical values in Lindemann uni-molecular chemical reaction-diffusion-heat conduction systems.The results of numerical simulations also showed that the differences of occurring critical values of Turing bifurcation led to multiple wave number values of spatially periodic structures of temperature field.Without doubt,these significant results should be considered in order to reasonably design,correctly choose the reactor type and optimally control chemical reactors.
