Previous conceptual studies have shown that the Accelerator-Driven Subcritical (ADS) system is capable of disposing the 115 tons of Minor Actinides (MAs) of the current U.S. Spent Nuclear Fuel (SNF) inventory. These studies used a homogenized subcritical assembly which is filled with liquid metal mobile fuel. The studies focused on selecting the physics parameters of the mobile fuel. This paper focuses on the development this ADS conceptual system including the physics and the thermal hydraulics of the subcritical assembly. The engineering requirements for a satisfactory operating performance of HT-9 ferritic steel structure material define the design criteria for the thermal hydraulics analyses. To avoid corrosion and erosion issues of the HT-9 material, the maximum surface temperature of the steel structure material is limited to less than 600 0C and the maximum liquid metal velocity at the steel structure surface is restricted to less than 3 m/s. The homogeneous concept which has the liquid metal mobile fuel circulate outside the subcritical assembly for heat removal purpose was considered first. However the required large mobile fuel inventory eliminates this concept for several reasons. Then the heterogeneous subcritical assembly with a separate liquid metal coolant was considered. Tube bundles are inserted into the original homogeneous subcritical assembly tank for the heat removal purpose. Two heterogeneous configurations were examined, which are different in the position of the liquid metal mobile fuel inside or outside the tube bundle. The physics calculations were performed to calculate the fission power distributions in these heterogeneous configurations. The heat transfer analyses were coupled with the reactor physics analyses to adjust the size and arrangement of the tube bundle distribution so that the design requirements are satisfied for both configurations.