An exact solution of the convective-diffusion equation for fully developed parallel plate laminar flow was obtained. It allows the derivation of theoretical relationships for calculating the Peclet number in the axially dispersed plug flow model and the concentration distribution perpendicular to the direction of the flow, provided that the corresponding solution of this model is known. The convective-diffusion equation was solved numerically using the implicit alternating-direction finite difference method. It was found that the theory developed is valid for Fourier numbers greater than 1.0. The results obtained can be used for the mathematical modelling of parallel plate process heat and mass exchangers, haemodialysers and flow-injection and continuous-flow manifolds with on-line dialysis units with parallel plate geometry.
Kolev, S. D., Kolev, S. D., & van der Linden, W. E. (1991). Laminar dispersion in parallel plate sections of flowing systems used in analytical chemistry and chemical engineering. Analytica chimica acta, 247(1), 51-60. https://doi.org/10.1016/S0003-2670(00)83051-2