In this study, a numerical model of a reciprocating magnetocaloric regenerator using a Halbach magnet array is developed by using ANSYS Fluent. The model consists of three components, namely (i) the Halbach magnet array, (ii) the magnetocaloric material, and (iii) the heat transfer fluid. It is studied in a 2-D domain due to the axisymmetric geometry of the physical model. In addition, a pressure difference is defined between the inlet and outlet sections of the fluid domain to maintain fluid flow. In the proposed computational scheme, a segregated approach is followed to consider spatial distribution of the magnetic field. Therefore, a two-dimensional magnetic field within the magnetocaloric material is computed using an analytical approach, and its results are integrated into ANSYS Fluent with a user-defined function (UDF). Hydrodynamic and heat transfer characteristics of the proposed regenerator model is evaluated under various Reynolds numbers and cycle durations. Moreover, the temperature drop at the cold side of the regenerator is represented in terms of the pressure difference, flow duration, and the diameter of Gadolinium (Gd) as the magnetocaloric material. For the current geometrical configurations, it is observed that the magnetic field varies from 0.4 T to 1 T within Gd. The highest temperature spans are measured as 8.7 K, 7.5 K and 7.2 K numerically for the cycle durations of 1.2 s, 2.2 s, and 4.2 s, respectively.