Assessment of TRU burning in a molten salt reactor moderated by zirconium hydride rods

•Proposed a TRU started-ZrH-MSR core design for TRU burning.•Investigated the core critical and burnup performances with consideration of TRU solubility limit for different fuel salts.•Optimized the TRU burning capacity of the ZrH-MSR under different neutron spectrums.•Evaluated the temperature feedback coefficient in the optimized ZrH-MSR during operation.