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 D-T is expressed by D-T = D-M(1 + lambda Pe(2)) and the coefficient lambda 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/D-M with a and U being the radius of tube and the mean fluid velocity on the shell side, respectively. The coefficient 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 A 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. (c) 2006 Elsevier Ltd. All rights reserved.