Abstract: An arc heater is one of the key facilities for ground testing of thermal protection materials which can generate high pressure, high enthalpy gas flow for extended periods. This paper established a three-dimensional mathematical model coupling the electromagnetic field, flow field, temperature field and radiation for an arc heater including the electrode chambers, constrictor section, and nozzle based on the magnetohydrodynamic theory. The model was validated using experimental and computational results from the literature. Furthermore, the mathematical model was used to investigate the effects of gas mass flow rate on the characte-ristics of the electromagnetic field, flow field, and temperature field inside the arc heater. The results show that: 1) The predicted voltage, pressure, mass-averaged enthalpy, and thermal efficiency are in good agreement with literature results, validating the reliability of the model; 2) The maximum values of arc chamber voltage, current density, Joule heating, and Lorentz force all increase with increasing gas mass flow rate, while the magnetic induction intensity and Lorentz force first increase and then decrease radially from the center to the edge; 3) The maximum velocities in the arc chamber and at the nozzle exit gradually decrease with the mass flow rate increasing from 0.07 kg/s to 0.40 kg/s, while the turbulent viscosity ratio downstream of the arc chamber increases by a factor of 7.8; 4) The maximum temperature in the arc chamber decreases from 10090 K to 8619 K as the mass flow rate increases, and the thermal efficiency reaches its maximum of approximately 63.3% at a mass flow rate of 0.3 kg/s.