The recent results of Hirano et al. [1] produced a record breaking trapped field of 1.61 T in a composite MgB2 ring, comprising copper plates and a soft iron yoke. Inspired by these results, a systematic numerical study was conducted to investigate the key parameters leading to the success of Hirano et al. [1]. Leveraging a finite-element method modelling framework in a commercial software package (COMSOL Multiphysics), we accurately repli- cated their experimental results [1]. Excellent quantitative agreement with the experimental data was achieved by making novel assumptions to the thermal physics, namely to that of the heat flow within the sample. The models are extended to investigate open & remaining questions; such as the influence of the iron yoke and the copper plates, and their interaction with the applied field. The results of the study illustrate how composite MgB2 rings may be optimised to trap even higher fields, and how the physics of their operation affect the trapped field distribution and magnitude. This submission disseminates the physics and modelling techniques used in detail, illustrating the novel modelling methods adopted to accurately simulate bulk composite MgB2 rings acting as trapped field magnets.