A model for the simulation of the shell-side convective diffusion of a solute in the hollow-fiber contactor with a regular arrangement of fibers is advanced. The model takes into account the impact of the fiber packing density on the shell-side constrained flow and solute transport. A system of periodic rows of parallel monodisperse fibers arranged normally to the laminar flow direction is considered as a model contactor. Flow and solute concentration fields are calculated from the numerical solution of the Navier-Stokes and convective diffusion equations over a broad range of the inter-fiber distances, Reynolds (Re) and diffusion Peclet (Pe) numbers. For the calculated fiber drag force and for the fiber Sherwood number (Sh) for high and intermediate Peclet numbers Pe >> 1 and at Re <= 50, the best-fit regression formulas are found. The fiber Sherwood number governs the contactor retention efficiency via E = 1 - exp(-4 alpha H Sh/a), where a is the fiber radius, H is the thickness of the layer of fibers, alpha is the packing density of fibers. For a dense fibrous medium, a retarded increase in Sh with Re at constant Pe and packing density is demonstrated. Fiber retention efficiency is shown to follow the fiber drag force, which makes it possible to estimate the solute retention efficiency of a contactor from its hydrodynamic resistance to the shell-side flow. A convective-diffusional transport of a solute in the hollow fiber contactor with a radial Stokes flow is also considered. (C) 2016 Elsevier B.V. All rights reserved.