Analysis of solid-phase axial heat conduction upon hot-spot formation in a one-dimensional microreactor

Abstract

A generalized one-dimensional model of a non-isothermal, monolithic microreactor is developed to investigate the impact of solid-phase axial heat conduction upon hot-spot formation. The model consists of a pair of first-order differential equations describing an exothermic reacting fluid which exchanges heat with the solid-phase that comprises the monolithic microreactor. Solid-phase axial heat conduction and exchange with an isothermal coolant is described by an additional second-order ordinary differential equation, with boundary conditions accounting for the possibility of conductive heat losses to adjacent fluid distribution manifolds. Criticality analysis is performed using both the explicit Van Welsenaure and Froment (VWF) criteria and implicit Morbidelli and Varma (MV) criteria. Results indicate that the VWF criteria applied to the limiting case of negligible axial heat conduction provides a reliable, albeit conservative, criteria for hot-spot prevention. Additionally, MV criteria applied to the case of sufficiently high axial heat conduction yields criteria for ensuring hot-spot formation. Analysis using MV criteria indicates that the introduction of mild solid-phase axial heat conduction promotes hot-spot formation so long as heat losses to manifolds is minimal.