Analytical solution of the convection-diffusion-reaction-source (CDRS) equation using Green's function technique

Abstract

Convection-diffusion-reaction-source (CDRS) equation has been used to model a variety of transport phenomena. While several numerical methods for solving the CDRS equation exist, there is a relative lack of analytical solutions for the CDRS problem for an arbitrary source term. This work presents a Green's function based analytical solution to a one-dimensional, transient CDRS equation with an independent source/sink that can be a general function of space and time. Results compare well with past work as well as an independent numerical simulation. The model presented here is simple, computationally fast, and does not suffer from stability problems commonly encountered in numerical solutions of the CDRS equation. Furthermore, the model is used to solve a representative CDRS problem. The model presented here may help analyze transport problems in various engineering applications, such as drug delivery, heat transfer in reacting systems, and air pollution dispersion. The analytical solution may also serve as a building block for solving more complicated problems such as transport in a multilayer body, as well as for verifying numerical simulation tools.