Kinetic theory analysis of heat transfer to a sphere from a stationary ionized gas

In many plasma-aided manufacturing applications, metallic or ceramic particles are introduced in thermal plasma. Thermal plasma is used as a heat source to heat and melt the solid particles. The plasma-particle heat transfer plays an important role in determining the quality of the products. Due to the high temperatures encountered in such applications, the Debye length may be smaller than the mean free path and the continuum approach can not be used to determine heat transfer. In this thesis, an analytical model of plasma-particle heat transfer is developed using a kinetic theory approach that is valid for continuum and non-continuum plasma. Two-sided electron velocity and temperature distributions and two-sided ion velocity distributions are used in the formulation. The governing equations for electrons and ions are obtained by taking the moments of the Boltzmann equation and are solved simultaneously with the Poisson's equation for the self-consistent electric field. The ion and electron number density distributions, temperature variations, and electric potential profile are obtained. The electron and ion flux to the particles surface is evaluated. Heat transport to the surface is calculated by accounting for all the modes of energy transfer including energy deposited at the surface due to the electron-ion recombination. The plasma-particle heat transfer under different operating conditions of plasma temperatures of 8000K to 15000K, particle radii of 20 mum∼100 mum and two commonly used background gases (Argon and Nitrogen) are studied. Results are first obtained for very low Knudsen number (where the neutral gas can be considered as continuum) and Debye length smaller than mean free path (where the charged species transport can not be assumed continuum). Results indicate that the contribution to heat transfer from electron-ion recombination is substantial at high plasma temperatures. Heat transfer results for small Debye length and small Knudsen number regime agree very well with the available empirical correlation.; The model is then extended to simulate low pressure conditions where the Knudsen number may not be small. The results for heat transfer from neutral gas show that the model correctly predicts the heat transfer behavior at all Knudsen numbers. At very low pressures (at large Knudsen numbers) the heat transfer increases with increase in pressure. However, at high pressures (at low Knudsen numbers, continuum conditions) the heat transfer from neutral gas is not affected by a change in gas pressure.