This work has been aimed at developing a mechanistic, transient, 3-D numerical model to predict the behavior of an evaporating thin liquid film on a non-uniformly heated cylindrical rod with simultaneous parallel and cross flow of vapor. Interest in this problem has been motivated by the fact that the liquid film on a full-length boiling water reactor fuel rod may experience significant axial and azimuthal heat flux gradients and cross flow due to variations in the thermal-hydraulic conditions in surrounding subchannels caused by proximity to inserted control blade tip and/or the top of part-length fuel rods. Such heat flux gradients coupled with localized cross flow may cause the liquid film on the fuel rod surface to rupture, thereby forming a dry hot spot. These localized dryout phenomena can not be accurately predicted by traditional subchannel analysis methods in conjunction with empirical dryout correlations. To this end, a numerical model based on the Level Contour Reconstruction Method was developed. The Standard k- turbulence model is included. A cylindrical coordinate system has been used to enhance the resolution of the Level Contour Reconstruction Model. Satisfactory agreement has been achieved between the model predictions and experimental data. A model of this type is necessary to supplement current state-of-the-art BWR core thermal-hydraulic design methods based on subchannel analysis techniques coupled with empirical dry out correlations. In essence, such a model would provide the core designer with a "magnifying glass" by which the behavior of the liquid film at specific locations within the core (specific axial node on specific location within a specific bundle in the subchannel analysis model) can be closely examined. A tool of this type would allow the designer to examine the effectiveness of possible design changes and/or modified control strategies to prevent conditions leading to localized film instability and possible fuel failure.