An integral‐spectral approach for reacting Poiseuille flows

Abstract

AbstractAn integral‐spectral formulation for laminar reacting flows in tubular geometry (tubular Poiseuille flows) is introduced and performed within an operator–theoretic frame‐work where the original convective‐diffusive differential transport problem coupled with reaction is inverted to give an integral equation. This equation is of second kind and of the Volterra type with respect to the axial coordinate of the tube with a kernel given by Green's function. Green's function is identified by a methodology that gives the Mercier spectral expansion in terms of eigenvalues and eigenfunctions of the Stürm–Liouville problem in the radial variable of the tube. Eigenvalue problems for both Dirichlet and von Neumann boundary conditions are solved in terms of analytical functions (Poiseuille functions) and compared with the values found in the literature. The groundwork is set for future applications of the methodology to solving a wide variety of problems in convective–diffusive transport and reaction. Examples with wall and bulk chemical reaction are given to illustrate the technique.