An argon magnetic fluid is a collection of free charged particles moving in random directions especially that is a weakly ionized argon discharge and on the average, electrically neutral. The 2-D numerical steady-state model of an argon magnetic fluid generator is presented to investigate the thermodynamic behaviors and the distribution of current density. The CFD codes, OpenFOAM, and FLUENT, are utilized in a modified form to model the argon magnetic flow inside the generator. Modeling a thermal magnetic fluid requires a combination of mutually related fluid dynamics and electromagnetic phenomena. With the appropriate thermophysical model, a pressure-based, steady-state, incompressible magnetic fluid solver based on OpenFOAM was originally developed. Meanwhile, FLUENT was expanded upon secondary development functions of user-defined scalar and user-defined function to develop magnetic fluid solution and make reference comparison. The results demonstrated that the numerical simulations obtained with the OpenFOAM solver were in good agreement with those from FLUENT. The highest temperature and velocity were both observed near the cathode region, with the main body temperature exceeding 6000 K. The anode region exerted a compressive effect on the temperature field and accelerated the MHD flow. The current density was primarily distributed in a columnar pattern, concentrated in the cathode region and exponentially decreasing along the axis towards the anode region, with a significant radial gradient.