The DEMOnstration fusion reactor is planned to be a first-of-a-kind nuclear fusion power plant to be built as the successor to ITER. The objectives of the design are the production of net electricity and operation with a closed fuel cycle. Replenishment of tritium fuel on-site will be imperative for the functioning of future commercial nuclear fusion reactors. Thus, accurate modelling of hydrogen transport and inventories within the reactor will be essential for safety issues and economic sustainability. The open-source FEniCS-based hydrogen transport code FESTIM [1] is used to perform multi-material, multi-dimensional and multi-physics simulations of a reactor sub-component: the breeding blanket. The design showcased is the Water-Cooled-Lithium-Lead (WCLL) concept [2], which utilises a liquid metal (LiPb) tritium breeding material. A companion fluid dynamics solver has been developed with FEniCSx to model the flow of the breeding material, accounting for MHD effects. The solver was verified using published analytical solutions [3, 4]. The resulting velocity field was coupled with FESTIM to accurately simulate hydrogen transport in both the liquid and structural domains of the component. [1] R.Delaporte-Mathurin, et al. NME, 21, 2019 [2] A.Del Nevo, et al. Fusion Eng. Des., 124, 2017 [3] J.Shercliff. Math. Proc. Camb. Philos. Soc, 49, 1953 [4] J.Hunt. J. Fluid Mech, 21, 1965