It has been proposed to build an accelerator for the production of tritium. A transient natural convection model of the accelerator blanket primary heat removal (HR) system was developed to demonstrate that the blanket could be cooled for a sufficient period of time for long-term cooling to be established following a loss-of-flow accident (LOFA). The particular case of interest in this work is a complete LOFA. For the accident scenario in which pumps are lost in both the target and blanket HR systems, natural convection provides effective cooling of the blanket for ∼68 h, and if only the blanket HR systems are involved, natural convection is effective for ∼210 h. The heat sink for both of these accident scenarios is the assumed stagnant fluid and metal on the secondary sides of the heat exchangers.