Heat pipe cooled reactors have gained significant attention as a research hotspot in small nuclear reactor technology due to their miniaturization and mobility features, making them suitable for various special applications like deep-space exploration, underwater scientific research, catalog research, and distributed power supply in remote areas. This study employs COMSOL Multiphysics to analyze the heat transfer and thermoelectric conversion characteristics of a static heat pipe reactor. We investigate the thermal-electrical coupling behaviors under local heat pipe failure condition and examine its combination with the whole thermoelectric system unloading condition. Under steady-state conditions, the heat pipes exhibit isothermal properties of 112.4 °C, 114.8 °C, and 117.3 °C in the side, center, and corner channels, respectively. In the condition of local heat pipe failure, it was assumed that five adjacent heat pipes failed. Consequently, the temperature gradient of the failed heat pipe at the center channel reached 485.1 °C. Despite the local heat pipe failure, the output power of the thermoelectric system still reached 120.8 kW, and the overall thermoelectric conversion efficiency remained at 12.1 %. When considering the coupling of local heat pipe failure with the unloading condition of the thermoelectric system, the maximum temperature of the reactor core increases by 675.8 °C. Additionally, the temperature gradient in the heat pipe adiabatic section rises to 517.3 °C in the center channel. The combined effect of overall temperature increasing and thermoelectric system unloading leads to open voltages ranging from 140.0 V to 149.0 V in the thermoelectric subsystem at different ports. The research findings suggest that the system temperature rise caused by the whole system unloading condition is more significant. Thus, considering the coupling effect of thermoelectric system unloading and heat pipe failure condition is conservative and crucial for a comprehensive analysis of the system behaviors. These results contribute to the understanding and optimization of heat pipe cooled reactors for various specialized applications.