An Alternate Mathematical Model for the TAP Technique for Numerical Integration

Source abstract

Abstract The mathematical modeling of the reactor in the TAP technique describes it as composed of zones of different diffusivity, and it makes the model linear by imposing boundary conditions of the continuity of concentration and flux at zone boundaries so as to be able to use a Fourier transformation technique to solve the equations. An alternative description of the reactor that uses a spatially non‐constant diffusivity to obviate the need to impose auxiliary boundary conditions in the regions where diffusivities change is proposed. The reactor equation is the mass balance equation without the simplification to the case of constant diffusivity, that is, without the diffusivity taken out of the differential operator. Computations based on it are compared with those of the linear model. The computed response curves of both models are similar, which indicates that the alternate model is equally good as a description of the reaction system. The alternate model is useful for modeling reactor systems with a variable cross‐sectional area or with temperature non‐uniformity.