In a recent article reported on the performance of a roof-top air conditioning unit by numerically predicting the thermal and hydrodynamic fields on the air flow side of the unit. This paper extends the work reported by and predicts the performance of the unit by analyzing the refrigerant flow side simultaneously with the air flow. The problem involves a turbulent multi-phase flow situation with condensation on the outer surface of the evaporator coil. Further, the heat transfer between the air flowing on the outer surface of the coil and the refrigerant flowing inside the pipes necessitates solving a conjugate heat transfer problem. Solutions are generated via a collocated unstructured finite volume method. A conformal mesh was generated at the common interface regions separating fluid and solid zones to account for the continuity of heat fluxes at these interfaces. Two sets of results are presented in this manuscript simulating a wet and a dry coil. Detailed numerical predictions are compared with a developed lumped analytical model and with available experimental data for a similar coil model and are found to be in good agreement. Complex turbulent flow fields were obtained in regions located upstream and downstream of the evaporator coil.