The use of Green's functions in the solution of a convective diffusion equation: Application to a fuel cell battery

Abstract

The diffusion equation with a constant mass flow term to account for bulk transport of heat or chemical species occurs in many practical problems, such as in heat transfer in fuel cell batteries, in chromatographic work with appreciable diffusion in the direction of flow, and in dispersion studies in fluids with and without reaction. The principal simplifying technique for the usual diffusion equation widely used in heat transfer is the product theorem due to Newman. Recently the construction of three-dimensional solutions from one- and two-dimensional problems was extended by Goldenberg. For the case of the diffusion equation with a linear term, for example, for diffusion with a first-order reaction, the transformation of Danckwerts is useful. It is shown how a change of the dependent variable, similar to that employed in the Danckwerts method, together with the tabulated Green's functions for the simple diffusion equation, can rapidly lead to many new solutions of the convective diffusion equation with a constant velocity. Then various product properties useful for analytical and graphical representations of two- and three-dimensional problems are established for the general, second-order, parabolic particl differential equation with constant coefficients. Examples having application in heat transfer in fuel cells are given.