The convection-diffusion equation with periodic boundary conditions Original Research Article

Solutions of the convection-diffusion equation with decay are obtained for periodic boundary conditions on a semi-infinite domain. The boundary conditions take the form of a periodic concentration or a periodic flux, and a transformation is obtained that relates the solutions of the two, pure boundary value problems. Solution representations, which do not seem to appear in the literature, are obtained. Explicit, simple forms are derived when the boundary condition consists of a single harmonic, and it is determined how the phase shift depends upon the diffusion, convection, and decay factors, as well as frequency.