Absorption refrigeration system is going through optimization. The evaporator is one of the core components of the absorption refrigeration system, and its optimization can be done by improving the wettability and reducing the uneven distribution of liquid film. Enhanced tubes are often helpful in mitigating the film thickness and ensuring proper wetting of the tubes, thus enhancing the heat transfer performance. Using a smaller tube diameter also significantly affects the heat transfer performance because of the increasing ratio of the developing boundary layer to the fully developed boundary layer. In this study, seven small-diameter (12.7 mm) tubes were used to optimize the performance of the evaporator. The parameters observed are as follows: falling-film Reynolds number (10–100), wall superheat (2.2–5.1 °C), and saturation pressure (0.9–1.20 kPa). The heat transfer coefficient exhibited a peak point at a falling-film Reynolds number, called transition Reynolds number (Retransition) mostly at a value of ~42. The wall superheat is increased by increasing the wall temperature and, as a result, the heat transfer coefficient remains unchanged; however, the heat flux increases almost linearly. The heat transfer coefficient increases with the increase in the saturation pressure. One of the fabricated tubes was tested with corrosion, and a negligible change in the heat transfer coefficient was observed when compared with the uncorroded tube. Both droplet and jet modes are observed when viewing the falling-film phenomena through a glass window. Smooth tube data reveal a reasonable comparison with the jet and droplet mode of Hu et al. Of all the tubes, the heat transfer coefficient of Tube_Z is the highest. Tube_Y1 exhibited the highest heat flux; however, Tube_Z exhibited the highest ratio of heat flux to friction factor. Empirical correlations were developed based on the current experimental perimeters, and correlations predicted the data within ±20%.