Dry patches could occur on the heat exchanger wall even if the initial liquid film covers the tube surface entirely. Here, we propose a simple three-dimensional model to predict the formation and evolution of dry patches in a water film coating on a horizontal tube, considering thermocapillary and evaporation of the liquid film. Results indicate that the film thickness distribution along the axis is not uniform, convex at ends and concaves at the center. Under the action of axial thermocapillary force, the growth rate of the dry patch in the circumferential direction is more significant than that in the axial direction and finally forms an elliptical shape. Comparative analysis reveals that the appearance of dry patches is delayed as the spray temperature decreases or Re increases. Tube radius has little influence on the drying of liquid film, which is not recommended to control dry patch formation by reducing the tube radius. This work could be beneficial to assist the feasibility design of falling film heat exchangers.