Chemical reactants typically are stored on board a vehicle in a condensed phase, to minimize vehicle weight and volume. These reactants often are gasified prior to introduction to the reaction chamber or cavity. Here we examine the gasification of a liquid stream by first forming a spray via a two-fluid (or pneumatic) atomizer, and then vaporizing the droplets during their transit of a coannular cylinder. The continuous, lateral transpiration (at an axially uniform rate, and at an axially uniform temperature) of inert, heated gas from the outer annulus helps to complete the vaporization of the droplets flowing through the constant-cross-section core of the circular cylinder. A simple, steady, isobaric, one-dimensional model of the convective/conductive heat transfer to, and the interphase drag on, monodisperse spherical droplets is examined for the case in which helium is added to a liquid stream to effect the atomization and the vaporization. In contrast with the more familiar scenario of the vaporization of hydrocarbon droplets in a gaseous oxidizer, here the droplets enter the vaporizer with internal temperature uniformly at nearly the boiling temperature. Also, the heat transfer from the gas phase to the droplets, and the ratio of gaseous-helium and liquid thermal conductivities, are such that the droplets undergo appreciable vaporization well before achieving uniform internal temperature at an adjusted value. Furthermore, the continuous lateral injection of heated gas to the core of the cylinder in which the droplets flow implies that the interphase-velocity slip may persist or even increase, with increasing downstream position within the cylinder. Under gas-phase-temperature constraints, we seek to identify convenient operating conditions consistent with virtually complete evaporation of the droplets prior to exit from the cylinder. We find that maximizing the interphase temperature and velocity slip for the large droplets present near vaporizer entry effectively promotes vaporization. Transpiration sustains velocity slip only where droplets typically have become too small for much convective enhancement of interphase heat transfer, and where the interphase temperature slip typically is relatively modest.