Non-expert summaryThe authors consider the steady laminar advective transport of a diffusive component released at the base of a narrow three-dimensional longitudinal open channel with non-absorbing side walls and rectangular or truncated-wedge-shaped cross-sections: the findings are relevant to heat and mass transfer applications in confined U-shaped or V-shaped channels (or trenches) such as might arise in the decontamination and cleaning of narrow gaps, crevices and boundary features on walls or other surfaces, and well as transport processes in chemical or biological microfluidic devices. The fluid flows along the channel in the laminar regime and there is no flux or slip on the side walls. Numerical simulations are conducted for various duct shapes and the rate of mass transfer from the base is calculated: this is used to evaluate the dimensionless mass transfer coefficient, the Sherwood number. The results for 3-D (constant cross section, long in the direction of flow) are compared favourably with results for a simplified, 2-D, calculation.