AN INTEGRAL-SPECTRAL APPROACH FOR REACTING POISEUILLE FLOWS

An integral-spectral formulation for laminar reacting flows in tubular geometry (tubular Poiseuille flows) is introduced and performed withi n an operator - theor eric framework where the original convectiue-dif fusive differential transport problem coupled with reaction is inverte d 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 wi th a kernel given by Green's function. Green function is identified by a methodology that gives the Mercier s spectral expansion in terms of eigenvalues and eigenfunctions of the Sturm - Liouville problem in th e 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-diffus ive transport and reaction. Examples with wall and bulk chemical react ion are given to illustrate the technique.