Analytical Solution of a Generalized Reaction-Diffusion Equation inside a Circular Reactor using Computer Algebra Systems

摘要

Using Computer Algebra Systems, certain problem of mass transfer is symbolically solved. The explicit solutions for a generalized reaction-diffusion equation with integral memory inside a circular reactor for two different boundary conditions, are derived using Maple. The method of solution is the Laplace Transform Technique with the Bromwich integral and the residue theorem. The solutions are obtained by means of certain algorithm for computer algebra. As a results we obtain both the explicit solution of the transport equation in terms of Bessel functions as the basic reproductive number for the reactor. We conclude that the transport problem that was considered, to despite to be linear, is symbolically non-computable due to the effects of the memory and the non-computable (symbolically) character of the fundamental theorem of algebra.