Convection-diffusion processes in a model hollow fiber membrane contactor with transverse radial convergent (divergent) laminar flow with a variable radial velocity have been studied. The model contactor has been an ordered system of monodisperse parallel fibers arranged perpendicular to the feed stream. A formula relating the absorption efficiency of the component in the coaxial fiber layer, depending on the direction of radial flow, to the fiber packing density and the Peclet number has been first derived.