Multidimensional Unsteady Solutions to the Convection-Diffusion-Reaction Equation with a Time Dependent Boundary Condition

Abstract

This paper provides analytical solutions to one, two and three-dimensional convection-diffusion equation with decay term, subjected to a time dependent and periodic boundary condition. These solutions are suitable benchmarks to asses the correctness of computational codes implemented for the problems of multidimensional reactive flows, which are of considerable interest to many fields of science and engineering. Tests are illustrated through computational codes and is remarked the feature of representing periodic oscillations in all dimensions considered.