Electrode Heating in a Wire-to-Plane Arc

A steady wire-to-plane electric discharge has been modeled in a prolate spheroidal coordinate system with the wire shape taken as a hyperboloid of revolution. A set of continuum conservation equations for the charged particle densities and temperatures together with Poisson’s equation for the self-consistent electric potential describe the steady electric discharge process. These equations have been solved numerically to obtain ion and electron densities, temperature distribution, and electrode heat fluxes. Particle densities show the main body of the arc is quasineutral bounded by space charge sheaths at both electrodes. The temperature is greatest in a region around the discharge axis about one-third of the distance from the wire to the plane. Strong electric fields are concentrated in the electrode sheaths. The heat flux to the wire is sharply peaked near the tip but on the plane it decays slowly away from the discharge axis. The knowledge of heat transfer from the arc to the electrodes is useful in determining arc parameters that govern the ball formation process used in wire bonding of microelectronic semiconductor chips as well as welding processes

Evaporation and Combustion of a Slowly Moving Liquid Fuel Droplet: Higher-Order Theory

The evaporation and combustion of a single-component fuel droplet which is moving slowly in a hot oxidant atmosphere have been analysed using perturbation methods. Results for the flow field, temperature and species distributions in each phase, interfacial heat and mass transfer, and the enhancement of the mass burning rate due to the presence of convection have all been developed correct to second order in the translational Reynolds number. This represents an advance over a previous study which analysed the problem to first order in the perturbation parameter. The primary motivation for the development of detailed analytical/numerical solutions correct to second order arises from the need for such a higher-order theory in order to investigate fuel droplet ignition and extinction characteristics in the presence of convective flow. Explanations for such a need, based on order of magnitude arguments, are included in this article. With a moving droplet, the shear at the interface causes circulatory motion inside the droplet. Owing to the large evaporation velocities at the droplet surface that usually accompany drop vaporization and burning, the entire flow field is not in the Stokes regime even for low translational Reynolds numbers. In view of this, the formulation for the continuous phase is developed by imposing slow translatory motion of the droplet as a perturbation to uniform radial flow associated with vigorous evaporation at the surface. Combustion is modelled by the inclusion of a fast chemical reaction in a thin reaction zone represented by the Burke-Schumann flame front. The complete solution for the problem correct to second order is obtained by simultaneously solving a coupled formulation for the dispersed and continuous phases. A noteworthy feature of the higher-order formulation is that both the flow field and transport equations require analysis by coupled singular perturbation procedures. The higher-order theory shows that, for identical conditions, compared with the first-order theory both the flame and the front stagnation point are closer to the surface of the drop, the evaporation is more vigorous, the droplet lifetime is shorter, and the internal vortical motion is asymmetric about the drop equatorial plane. These features are significant for ignition/extinction analyses since the prediction of the location of the point of ignition/extinction will depend upon such details. This article is the first of a two-part study; in the second part, analytical expressions and results obtained here will be incorporated into a detailed investigation of fuel droplet ignition and extinction. In view of the general nature of the formulation considered here, results presented have wider applicability in the general areas of interfacial fluid mechanics and heat/material transport. They are particularly useful in microgravity studies, in atmospheric sciences, in aerosol sciences, and in the prediction of material depletion from spherical particles

Breakdown of a Wire-to-Plane Discharge: Transient Effects

A wire-to-plane discharge during the early phases of breakdown has been studied. The discharge has been modeled in a prolate spheroidal coordinate system with the wire shape taken as a hyperboloid of revolution. Four simultaneous coupled, time-dependent, nonlinear partial differential equations describe the electrical discharge. These are the conservation equations for ion and electron densities, the energy equation for electron temperature, and Poisson’s equation for the self-consistent electric field. By solving this formulation subject to appropriate initial and boundary conditions, charged particle densities and temperature variations have been obtained as the ionization progresses in the discharge. The results show that both the electron temperature and the charged particle densities increase with the progress of ionization. The effect of different wire polarities is also examined. With a positive wire polarity, the increases in electron temperature and charged particle densities are confined to regions of the discharge in the vicinity of the wire tip. With a negative wire polarity, the breakdown occurs in the entire gap at a faster rate than with a positive wire polarity. The wire polarity affects the magnitude of energy transfer between the particles