The evaporation of a volatile liquid from a slot-like cavity situated in the lower wall of a flat rectangular duct was studied both numerically and experimentally for laminar, fully developed airflow in the duct. The capillarity-induced curvature of the liquid surface was determined analytically and was found to be well represented by a circular arc. Owing to the surface curvature, the solution domain was partially rectangular and partially cylindrical. Interlocking and overlapping rectangular and cylindrical finite-difference grids were used for the numerical work, and the resulting evaporation rates agreed to within 0-3% with the experimental data, depending on the distance between the top of the cavity and the liquid surface. This excellent level of agreement demonstrates that for problems which do not fit neatly into a single coordinate system, highly accurate results can be obtained without having to resort to complex numerical methods. Supplementary numerical work demonstrated that the duct flow upstream and downstream of the cavity opening can be omitted from the solution domain without affecting the accuracy of the evaporation rate results. The fluid flow in the space between the top of the cavity and the curved liquid surface differed from that of the classical flat-bottomed, lid-driven cavity in that the corner eddies were absent.