An analysis is performed of the strongly coupled heat and mass transfer processes which result from sublimation of mass from the walls of a duct into a flowing gas, the latent heat being provided solely by convective transfer from the gas. The flow is assumed to be laminar and hydrodynamically developed. Results are given for the streamward variations of the bulk and wall temperatures and mass fractions, of the heat and mass transfer rates, and of the local heat transfer coefficient. Representative temperature and mass fraction profiles are also presented. Entrance lengths characterizing the near approach to fully developed conditions are tabulated. Comparisons are made of the present results (based on a parabolic velocity profile) with those based on a slug flow velocity profile. A subsidiary analysis using the Lévěque model is also performed and the results compared with those of the principal solution.