Despite the high theoretical performance limits of magnetic refrigeration systems, coefficient of performance (COP) of these systems can be lower due to abortive magnet and magnetocaloric material (MCM) assembly orientation and space limitation. To address both of these problems, a rotary-type magnetic cooling system with varied geometric properties was modelled and simulated. Heat transfer from the MCM, which was selected to be gadolinium (Gd), to the working fluid, was considered as volumetric energy generation. Three different geometries of disc-MCM assembly were studied where the inner and outer radii were selected as 5, 10, 15 mm, and 10, 15, 20 mm, respectively. It was observed that the gradient between steady-state temperature and the room temperature decreases with decreasing gadolinium-to-disc area ratio. Conductive heat transfer through the thickness of the disc was found to be inconsiderable compared with the convective heat transfer through the top surface.