A one-dimensional model of heat and mass transfer between gas and liquid streams in direct contact within a duct has been solved using power series expansions for the unknown functions which describe the stream wise evolutions of the bulk temperatures, the mass ratio in the gas phase and the liquid mass flow rate. The model is based on the assumptions of constant heat and mass transfer coefficients and the existence of a thin saturated layer between the two streams. The solution can be used for any axially invariable geometrical configuration, for any combination of fluids and for laminar or turbulent flow conditions. It has been applied to air and water systems to investigate the effects of different entry conditions and adiabatic or non-adiabatic walls on the performance of evaporators and condensers with parallel or counter-flow arrangements. (C) 2004 Elsevier Ltd. All rights reserved.