Taylor dispersion coefficients for laminar, longitudinal flow past arrays of circular tubes

The problem of determining shell-side Taylor dispersion coefficients for a shell-and-tube configuration is examined in detail for both ordered as well as disordered arrangement of tubes. The latter is modeled by randomly placing N tubes within a unit cell of a periodic array. It is shown that shell-side Taylor dispersion coefficient DT is expressed by DT = DM(1 + λPe2) and the coefficient λ is divergent with N, where DM is the molecular diffusivity of solute on the shell side and Pe is the Peclet number given by aU/DM with a and U being the radius of tube and the mean fluid velocity on the shell side, respectively. The coefficient λ depends on the spatial average and the fluid velocity weighted average of the concentration of solute on the shell side. The behavior of the coefficient λ with N arises due to logarithmically divergent nature of concentration disturbances caused by each tube in the plane normal to the axes of the tubes. An effective-medium theory is developed for determining conditionally-averaged velocity and concentration fields and hence the shell-side Taylor dispersion coefficients. Its predictions are compared with the results of rigorous numerical computations. The present study also presents formulas for determining the shell-side Taylor dispersion coefficients for square and hexagonal arrays of tubes with cell theory approximations.