A mathematical model is presented to describe the heat transfer and fluid flow in a magnetron plasma torch, by means of a commercial computational fluid dynamics (CFD) code fluent. Specific calculations are presented for a gas-mixing system (i.e., an argon plasma discharging into an air environment), operating in a laminar mode. Numerical results show that an external axial magnetic field (AMF) may have a significant effect on the behavior of an arc plasma, i.e., the AMF will impel the plasma to retract axially and expand radially. In addition, the use of an AMF induces a strong air indraft at the torch spout, and the air mixing with the argon gas results in a marked increase in arc voltage. An increment in the amount of the oncoming argon gas restrains the quantity of the air indraft, and this should be responsible for a lower arc voltage in such an AMF torch when a larger gas inflow is used.