Nonisothermal reaction-diffusion systems

The basic equations for an unsteady-state process of one-dimensional (in the -direction) heat and mass transport with a simultaneous chemical reaction in a porous catalyst pellet are 

Coupled systems of chemical reactions and transport processes 

The linear nonequilibrium thermodynamics approach can provide a quantified description of the fully coupled phenomena for systems in the vicinity of global equilibrium. 

In a multicomponent fluid, a species can be driven not only by its own thermodynamic force (its own concentration gradient) but also by concentration gradients of all the other species. Flow of species j in an n multicomponent fluid system is 

For ideal fluid mixtures, the Maxwell-Stefan equation yields 

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Nonisothermal reaction-diffusion systems represent open, nonequilibrium systems with thermodynamic forces of temperature gradient, chemical potential gradient, and affinity. The dissipation function or the rate of entropy production can be used to identify the conjugate forces and flows to establish linear phenomenological equations. For a multicomponent fluid system under mechanical equilibrium with n species and A r number of chemical reactions, the dissipation function 1 is... 

Figure 9.4. Dynamic behavior of thermodynamically coupled nonisothermal reaction-diffusion system of catalytic oxidation of CH3OH to CH20 (a) concentration surface, (b) temperature surface. The parameters used are in Table 9.1.

Modeling of spatiotemporal evolution may serve as a powerful complementary tool for studying experimental nonisothermal reaction-diffusion systems within a porous catalyst particle and a membrane. The linear nonequilibrium thermodynamics approach may be used in modeling coupled nonisothermal reaction-diffusion systems when the system is in the vicinity of global equilibrium. In the modeling, the information on coupling mechanisms among transport processes and chemical reactions is not needed. 

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