An Integral Equation Formulation for Solving Reaction-Diffusion-Convection Boundary-Value Problems

Abstract

Many interesting problems that include convective transport arise in chemical reactor engineering (for example, tubular reactors). To solve these boundary-value problems, finite-difference schemes with a type of discretization of the convection term have been traditionally used. Some controversy about the discretization form of the convection term has arisen because of the different possibilities, including backward, forward and central discretizations. To overcome this problem, the usage of Green's function formulations for the numerical solution of typical chemical engineering problems with both linear and nonlinear kinetics, diffusion and convection phenomena, is presented. A distinctive feature of the proposed scheme is that boundary conditions are exactly incorporated. The results show that the integral formulation is, in general, superior in accuracy to the different finite-differences schemes. That is, more accurate calculations of the performance factor are obtained in terms of less mesh points and computer time.

Convective heat transfer in a channel partially filled with a porous medium

“…Therefore, it is necessary to implement an iterative scheme to find the velocity field. This type of implicit integral formulations have been utilized, for example, in solving transport-reaction mass problems with linear and nonlinear kinetics in basic geometries [43,45,46].…”

Transferencia de calor entre un medio poroso y un fluido

“…Por lo tanto se requiere de un esquema iterativo para encontrar el campo de velocidad. Este tipo de formulación integral implícita ha sido utilizado, por ejemplo, para resolver problemas de transporte de masa que involucran reacción química con cinéticas lineales y no lineales (Valdés-Parada y col., 2007a, 2008a en geometrías simples.…”