Modal analysis of convection with axial diffusion

Abstract

The one‐dimensional model for convection with diffusion and with a source term for mass or energy generation or interchange is analyzed for the eigenvalues and the corresponding spatial eigenmodes as a function of the Peclet number. It is shown how the modal analysis of the source case, when the source coefficients for heat exchange and chemical reaction are spatially independent, is directly related to the no source solution. Numerical examples of determining the source term coefficient are included. These solutions form a base to discuss dynamic characteristics and stability and to which solutions for spatially dependent coefficients can be compared.