# Asymptotic and numerical studies of plasma arc heat transfer and phase change heat transfer

#### Abstract

Two important heat transfer processes--plasma arc heat transfer and phase-change heat transfer--have been examined by asymptotic and numerical methods. With plasma arc heat transfer, the breakdown of a wire-to-plane discharge has been critically examined. The conservation equations for charged particle densities, electron temperature and Poisson's equation for the self-consistent electric field have been solved simultaneously. The transient variations of the charged particle densities, temperature distribution, and the electric field have been calculated. A two region model has been developed to study the electrode heat transfer in the subsequent steady wire-to-plane arc. The temperature distributions and the electrode heat fluxes have been calculated. The effect of wire polarity on the heat transfer from the arc to the electrodes has been ascertained. The results obtained are in good agreement with those of experimental investigations. The study has direct applications in the manufacturing of semiconductor chips. In this context, an evaluation of thermally induced stresses in microelectronic components has also been provided to aid in the assessment of mechanical reliability under conditions of accelerated thermal cycling. In the phase-change heat transfer aspect of this dissertation, study of an isolated fuel droplet evaporation and combustion has been described. Drop translation is considered as a small perturbation over strong radial evaporation. Owing to large rates of evaporation the complete flow field is not in the Stokes regime. A singular perturbation technique is used to analyze this problem with the translational Reynolds number $\epsilon$ taken as the small parameter in the perturbation scheme. The flow field, the species distribution and the temperature distribution have been calculated up to and including $O(\epsilon\sp2)$ by matched asymptotic expansions for an n-heptane droplet burning in air. Results for the temporal variations of the drag force acting on the droplet and the heat/mass transfer at the liquid-gas interface have been provided. Ignition and extinction characteristics may be derived from the theory described herein. Details of the complicated mathematical procedures required for this study have been included.

#### Subject Area

Mechanical engineering

#### Recommended Citation

Jog, Milind Arun, "Asymptotic and numerical studies of plasma arc heat transfer and phase change heat transfer" (1993). Dissertations available from ProQuest. AAI9321412.
https://repository.upenn.edu/dissertations/AAI9321412

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