A new approximate solution which bridges the gap between the classical theories of Graetz and Leveque for heat/mass transfer in channel flow is presented. The results include expressions, uniformly valid in the axial direction, for the mixing-cup concentration (or temperature) profile < c > when transport towards the wall is slow (Dirichlet limit), and for the Sherwood number Sh when the wall flux can be considered uniform (Neumann limit). The technique employed provides insight into the mathematical structure of both quantities < c >(or conversion XR) and Sh identifying explicitly the contributions from fully developed and developing behaviors, while maintaining accuracy in the transition region. Criteria to bound the different convection-diffusion regimes are suggested, which critically systematize previous results. These results are important for model selection in the design and simulation, among others, of heat exchangers and wall-coated microreactors where fast heterogeneous reactions occur. (C) 2011 American Institute of Chemical Engineers Lambda IChE J, 58: 18801892, 2012