This article deals with the numerical simulation of a two-dimensional instantaneous heat and mass transfer processes within a commonly used intermetallic compound (a.k.a. Mischmetal) packed in a unit disc of an annulus-disc reactors, during hydrogen gas desorption. Using the finite volumes technique bundled in the OpenFOAM® CFD code, temperature and amount of desorbed hydrogen and their time-averaged quantities inside the metal-hydride packed bed are obtained for various temperatures of fluids used in heat transfer, and several outlet pressure magnitudes. Using a set of numerical simulations, we have emphasized the impacts of both parameters on metal-hydride reactor performance related to discharging time. An excellent accord was recorded for the present simulations results compared against the literature-reported experimental data [20].