Towards computationally-efficient modeling of transport phenomena in three-dimensional monolithic channels

In general, three-dimensional (3D) non-isothermal models for monolithic channels that seek to capture the local transport phenomena are computationally expensive. In this regard, we present a reduced model for a monolithic channel that reduces the computational cost, whilst preserving the 3D geometry and all of the essential physics - this is accomplished by exploiting the inherent slenderness of the monolith channel, coupled with scaling arguments, leading-order asymptotics and a fast space-marcher. The model takes into account conservation of mass, momentum, species and energy coupled with chemical kinetics, and is demonstrated for a three-way reaction mechanism for treatment of automotive exhaust. The results of the reduced model are verified against those of the full model and validated with axial temperature distributions for an experimental square channel. Overall, memory requirements and computing time are reduced by around 2-3 orders of magnitude as compared to the full set of equations. Finally, we discuss the suitability of the reduced model for reactor-scale modeling and extensions for transient simulations and other slender chemical engineering systems.