Heat transfer to a spherical particle in a flowing plasma

Heat flux to a sphere moving in a high-pressure plasma is considered. The sphere is electrically insulated and it is at floating potential. Numerical calculations are performed for conditions typical for plasma arc spraying: the sphere diameter is from tens to hundreds of micrometres, its velocity is on the order of hundreds of metres per second, plasma gas-argon of atmospheric pressure. It is shown that (a) the standard gas-dynamic method to calculate, Q, heat flux to a sphere Q = κRΔTNu, Nu = 2 + 0.6Re1/2Pr1/3 does not describe Q correctly because it grossly overestimates heat conduction by electrons (κ is the total plasma thermal conductivity, R is the particle radius, ΔT is the temperature difference between plasma and the particle, Nu, Re and Pr are Nusselt, Reynolds and Prandtl numbers, respectively); (b) heat flux is not evenly distributed over the particle's surface: the side of the particle that faces the upstream plasma is more heated than the opposite side and (c) ionization in the particle proximity could be important under conditions typical for plasma arc spraying.