The Positive Column of the Nitrogen Arc at Atmospheric Pressure. II

Abstract

Further work with the theory of the positive column, previously reported by the authors, has made possible its extension to include convection in the power loss. The convection heat loss function employed in this extended theory was developed empirically subject to certain restrictions imposed by dimensional analysis, and subject to the need for describing accurately existing experimental data on the arc itself. These restrictions have proved to be sufficiently rigid to limit greatly the choice in form for the heat loss function. Hence the authors feel some confidence in the view that the ultimate theoretical solution of the convection heat loss problem must yield a heat loss function very nearly identical with the one developed here. The inclusion of convection makes it possible to satisfy the customary boundary conditions in the differential equation governing the positive column, thus removing the necessity for employing any artifice such as the assumption of extreme power dissipation in the solution of the arc problem. The theory yields values of the power dissipation per unit length, over the range from one to ten amperes, and values of the arc temperature, which are in good agreement with existing experimental data. Values of the visual arc radius, for comparison with those obtained experimentally, are not available from the theory because of lack of detailed knowledge concerning the distribution of radiation in the arc. An average radius is computed, however, which should, and does, show the same general trends as those exhibited by the visual arc radius as determined from experiment. The present theory provides a satisfactory solution of the arc problem so long as the power loss by radiation constitutes a negligible fraction of the whole.