This study examines the effects of particle size and heat pipe angle on the thermal effectiveness of a cylindrical screen mesh heat pipe using silver nanoparticles (Ag) as the test substance. The experiment investigates three different particle sizes (30 nm, 50 nm, and 80 nm) and four different heat pipe angles (0°, 45°, 60°, and 90°) on the heat transmission characteristics of the heat pipe. The results show that the thermal conductivity of the heat pipe increased with an increase in heat pipe angle for all particle sizes, with the highest thermal conductivity attained at a 90° heat pipe angle. Furthermore, the thermal resistance of the heat pipe decreased as the particle size decreased for all heat pipe angles. The thermal conductivity measurements of the particle sizes—30, 50, and 80 nm—were 250 W/mK, 200 W/mK, and 150 W/mK, respectively. The heat transfer coefficient values for particle sizes 30 nm, 50 nm, and 80 nm were 5500 W/m2K, 4500 W/m2K, and 3500 W/m2K, respectively. The heat transfer coefficient increased with increased heat pipe angle for all particle sizes, with the highest heat transfer coefficient obtained at a 90° heat pipe angle. The addition of Ag nanoparticles at a volume concentration of 1% reduced the thermal resistance of the heat pipe, resulting in improved heat transfer performance. At a heat load of 150 W, the thermal resistance decreased from 0.016 °C/W without nanoparticles to 0.012 °C/W with 30 nm nanoparticles, 0.013 °C/W with 50 nm nanoparticles, and 0.014 °C/W with 80 nm nanoparticles. This study also found that the heat transfer coefficient increased with increased heat pipe angle for all particle sizes, with the highest heat transfer coefficient obtained at a 90° heat pipe angle.