Green's Functions of a diffusion equation

In diffusion modeling, it is often imperative to solve partial differential equations describing the concentration distribution of a substance released into a fluid subject to various kinds of initial and boundary conditions. The use of Green's theorems to solve such problems is one of the most powerful and promising methods because there are almost no limitations on the type of source conditions and functions depicting boundary values once the corresponding Green's function is obtained. Green's functions for a steady state, three‐dimensional turbulent diffusion equation with variable coefficients are, therefore, systematically presented for Dirichlet and Neumann boundary value problems in a number of important regions. Within the framework of power law approximations for velocity and diffusivities, solutions for most of the diffusion problems can be obtained by the proper choice of Green's functions given in this letter and the adroit manipulation of an integral.