An unsteady model of condensation flow in capillary regime inside a cylindrical tube was developed, based on a two-fluid approach. The model takes into account the coupling between the liquid film zone (where the quality is low) and the nearly hemispherical meniscus which is present at the end of the condensation region. Numerically, a major difficulty is that this type of problem has a free boundary condition. Indeed the end location of the two-phase zone is the result of all the heat exchanges occurring upstream of this area. To overcome this difficulty a mathematical representation was specifically developed. The unsteady model presented is based on five dimensionless numbers characterizing this type of flow. A comparison between the results of this model and those of a previously developed stationary model is made. An excellent agreement is obtained. The presence of self-sustaining oscillations due to the intrinsic mechanisms of condensation are also obtained numerically. The variation of the Nusselt number with the boiling number is then determined and presented. These results complement the previous study by determining the frontier between the stable and unstable situations. The atypical behaviour of the Nusselt number preceding the onset of instability is also analyzed.

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