In this study, the effect of the tube inclination angle on simultaneous condensation inside and pool boiling outside a smooth tube is investigated numerically. Such conjugate phase-change phenomena happen in many heat exchangers, particularly in passive heat removal systems. The simulated domain is a pool filled with water liquid at atmospheric pressure, with a submerged tube with inner and outer diameters of 19 mm and 25 mm respectively. The fluid inside the tube is considered to be the steam at the saturation temperature of 250 °C, which is a very common operating condition in many heat removal systems. The flow field is considered to be turbulent, unsteady and three dimensional. The effect of conduction through the tube thickness is also taken into account. The Eulerian-Eulerian multiphase flow approach is utilized to express the governing equation of the problem. ANSYS FLUENT 17.1 is also used to solve the governing equations. The effects of various parameters, such as tube orientation, steam mass flux and inlet steam quality on the condensation and pool boiling heat transfer coefficients, are investigated. The results show good agreement with the available experimental data. The condensation heat transfer coefficient is found to increase with an increase in the inlet steam quality and steam mass flow rate. The results of the effect of inclination on the heat transfer coefficient are also compatible with the previous experimental works. Moreover, the results show that there is a partial maximum point for the total heat transfer coefficient at an inclination angle between θ = −60° and θ = −30°.