A potential and stream function analysis of two-dimensional steady-state convective diffusion equations involving Laplace fields

Abstract

A special technique in solving steady-state two-dimensional convective diffusion equations involving external force fields having Laplace potentials is presented. The technique uses the fact that it is possible to find a conjugate stream function to the potential and the two can thus be considered as independent coordinates. The convective diffusion equation can be transformed into the potential and stream function coordinates and the resulting equation is separable in term of these two new coordinates. Two examples are illustrated. A pseudo-two-dimensional problem is also presented to show the usefulness of the technique even when not all requirements are met. Relations with Helmholtz and Schrödinger equations are discussed.