This paper develops models for steady-state, fully developed, laminar flow in rectangular channels with internal coaxial solid cylinders. By casting and solving the parallel -flow momentum equation in a dimensionless setting, correlations are derived for the friction factor f and represented as Ref where Re is the Reynolds number. The correlations consider three positions for the internal cylinder. The cylinder may be in the center of the rectangular channel, in the corner of the channel, or resting at the middle of the channel floor. The correlations incorporate channel aspect ratios in the range 0.1 < a < 1.0. The cylinder -diameter aspect ratios beta range from being vanishingly small to being large enough to touch the channel walls. Although the results are general, the study is motivated by considering the effects of diagnostic probes within small channels of catalytic monoliths. (C) 2016 Elsevier Ltd. All rights reserved.