Channel Flow

Abstract

There are many chemically reacting flow situations in which a reactive stream flows interior to a channel or duct. Two such examples are illustrated in Figs. 1.4 and 1.6, which consider flow in a catalytic-combustion monolith [28,156,168,259,322] and in the channels of a solid-oxide fuel cell. Other examples include the catalytic converters in automobiles. Certainly there are many industrial chemical processes that involve reactive flow tubular reactors. Innovative new short-contact-time processes use flow in catalytic monoliths to convert raw hydrocarbons to higher-value chemical feedstocks [37,99,100,173,184,436, 4471. Certain types of chemical-vapor-deposition reactors use a channel to direct flow over a wafer where a thin film is grown or deposited [219]. Flow reactors used in the laboratory to study gas-phase chemical kinetics usually strive to achieve plug-flow conditions and to minimize wall-chemistry effects. Nevertheless, boundary-layer simulations can be used to verify the flow condition or to account for non-ideal behavior [ 1471. The objective in this chapter is to develop boundary-layer approximations that consid-erably simplify the governing equations and facilitate computational modeling. Originally conceived by Ludwig Prandtl , the boundary-layer approximations themselves are very well known in fluid mechanics and have been widely used since the early 1900s [210,350,429]. Originally boundary-layer theory was developed for external flow over surfaces for appli-cations such as airplane wings. Generally speaking, one can anticipate boundary-layer behavior in situations where there is a dominant flow direction. Under such conditions, it is often the case that convective transport in the principal flow direction dominates over diffusive transport in that direction. However, there may well be substantial cross-stream diffusive and convective transport. Beginning with the Navier-Stokes equations and a particular flow geometry, we seek scaling arguments that permit neglecting some terms in favor of others. It should be recog-nized that this a fundamentally different route than was taken in the previous chapters on