First of all, I would like to thank you all for your help! My question is like this: It's a plasma spraying problem. Argon are heated and accelerated between a cathnode and a anode in a slim cylinder which is axisymmeteric, then the they are sprayed out toward the atmosphere(air) as free flame. Inspite of the complex phenomena, I just want to know the temperature and velocity field distribution of the flame in air. Thanks

(1). You can do it in two steps. (2). The first step: Assuming that it is air-to-air, compute the free jet problem with given jet velocity and temperature. In this way, you can get the jet velocity and the jet temperature decay or distributions. (3). Then you can compute the free jet mixing between argon and air, with given argon jet velocity and temperature. (4). Chemical reactions and radiation? Well, it's too complicated.