This research conducted thermal-hydraulic analysis on a thermal shield of the National Bureau of Standards Reactor (NBSR) using computational fluid dynamics (CFD) techniques with ANSYS 19.2. The NBSR thermal shield is a hollow, cylindrical water-cooled lead-steel structure surrounded by a biological shield made of heavy concrete. At full-power operating conditions, 210 kW of heat load deposits on the thermal shield. To prevent excessive heating of the shield, this heat must be extracted by a water-cooling system and convection with the surroundings. The thermal shield cooling system is comprised of 180 copper tubes (3/8 K type) running with water at 2 gal/min and with an inlet temperature of 308.15 K. Blocking of the coolant flow in embedded flow channels of the shield may cause the shield material to melt. To define the safe operating conditions of the nuclear reactor, the thermal shield model was examined across a range of flow rates with the maximum and minimum flow rates being 4 and 0.5 gal/min, respectively. With consideration of the creep temperature of lead as a threshold, from this research, it is determined that the maximum allowable number of consecutive tubes that can be blocked is 11. The cooling performance of various water-based Al, Cu, Al2O3, CuO, SiO2, SiC, and TiO2 nanofluids was also studied, but the results showed that water was more effective than nanofluids in cooling the thermal shield. Further, a two-phase boiling analysis was carried out to predict the vapor formation in the shield cooling system, and it was observed that water started vaporizing in the shield's upper-section tubes when the flow rate was reduced to 0.2 gal/min.