Unsteady-state liquid diffusion in laminar flow in a circular tube

Abstract

A technique was developed for solving the mathematical model describing unsteady-state diffusion in a Newtonian liquid in steady-state laminar flow in a circular tube. The process of interest in this work was one in which the Péclét numbers were very high and axial diffusion effects could, therefore, be neglected. The mathematical model describing this process was a partial differential equation with three independent variables and its associated boundary conditions. The method of solution used the Laplace transform, followed by either separation of variables or finite difference calculations, depending on the magnitude of the parameters involved. This method has the advantage that it eliminates the complex finite difference techniques and their associated stability and convergence problems which must otherwise be employed for exact numerical solutions of boundary value problems in three independent variables. The solution obtained in this work showed excellent agreement with experimental data collected in the present work and in previous research. This technique can be applied to other mathematical models of similar form describing transport problems in unsteady-state laminar flow and should make exact numerical solutions to this class of problems more easily obtainable.