This paper investigates coupled phase changes by forced convection from co‐current flows of liquid films and vapour‐air mixtures in a tubular heat exchanger. Evaporation occurs in the inner tube and condensation in the annulus region. Heat and mass transfers in the liquid films and the vapour‐gas mixtures are described by the conservation equations of momentum, energy, and diffusion. An appropriate change of coordinates is introduced in order to obtain a computational mesh with straight liquid‐mixture interfaces along the walls. The governing equations are discretized by an implicit finite differences method and solved using an efficient numerical methodology. The distributions of axial velocity, temperature, and vapour concentration in all regions of the tubes are determined from iterative procedures with a high convergence rate. The current analysis also provides the axial evolutions of film thicknesses, heat flux, condensation, and evaporation rates in the whole domain. In addition, the effects of the inlet parameters of Reynolds number, relative humidity, pressure, and liquid flow rate on the heat transfer characteristics, and the evaporation and condensation rates are also investigated.