Solution of Diffusion Problems

Abstract

In analogy to the kinematics of fluid mechanics, the principle of superposition of singularity solutions (sources, sinks, doublets, etc.) is applied to the solution of diffusion problems, involving various conditions. Due to the parabolic character of the diffusion equations in contrast to the elliptic (or hyperbolic) character of the equations of fluid mechanics, the fundamental concepts, like source, doublet, streamline, line of constant contamination, have to be rederived and illustrated. The composition of such singularity solutions, which must fulfill specific boundary conditions, leads to an integral equation, whose solution is indicated.