Convective Diffusion Equation in Two and Three Dimensions

Chemical reaction and mass transfer are two unique phenomena that help define chemical engineering. Chapter 8 described problems involving chemical reaction and mass transfer in a porous catalyst, and how to model chemical reactors when the flow was well defined, as in a plug-flow reactor. Those models, however, did not account for the complicated flow situations sometimes seen in practice, where flow equations must be solved along with the transport equation. Microfluidics is the chemical analog to microelectro-mechanical systems (MEMS), which are small devices with tiny gears, valves, and pumps. The generally accepted definition of microfluidics is flow in channels of size 1 mm or less, and it is essential to include both distributed flow and mass transfer in such devices. 

This chapter uses FEMLAB to solve problems involving two- or three-dimensional flow (2D or 3D) and diffusion of mass and/or heat. Convection and diffusion of mass 

Introduction to Chemical Engineering Computing, by Bruce A. Finlayson Copyright 2006 John Wiley Sons. Inc. 

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Fluid Flow in Two and Three Dimensions 11 Convective Diffusion Equation in... 

The concentration profile may be independent of time and vary in more than one dimension thus a two-dimensional or three-dimensional spatial problem results. Occasionally a system is encountered where rapid convection occurs perpendicular to the electrode surface so that diffusion is negligible in that coordinate. By rearranging equations (76) and (77) and normalizing the concentration, the mass transport to a ChE at steady state is given by (110). 

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