Hyperbolicity of reaction‐transport processes

Abstract

In this manuscript, common chemical engineering transport-reaction systems are modeled by taking into consideration the inertia in the transport phenomena, leading to hyperbolic partial differential equations (PDEs), which have finite speed of propagation. The findings provide the derivation of the hyperbolic transport-reaction PDEs and a direct comparison with their corresponding dissipative parabolic PDEs. The stability analysis of the dynamical systems is considered and complemented by numerical simulations for typical processes, such as the heat diffusion in a slab, transport-reaction inside a chemical reactor, and a phase change problem. The results demonstrate the effects associated with the modeling and/or limits of the approximation used in the derivation and application of the hyperbolic PDE for transportreaction systems, and the difference between the dynamics of this type of equation and the generally used parabolic PDEs.