A method for computing the radial temperature distributions in wall-stabilised arcs is developed and is applied to the treatment of D-line emission from a sodium arc lamp. The method adopts a radial temperature distribution containing two free parameters whose values are derived from two coupled nonlinear equations, one describing the energy balance on the arc axis, and the other the integrated energy balance. The radiative terms in the energy balance equations are obtained from a solution of the exact transfer equation.
The orthogonal collocation method is applied to the study of wall-stabilised plasma arcs. The numerical implementation of this method is simpler and faster than that of finite difference methods of comparable accuracy. The solutions obtained agree with experiments and with previous finite difference calculations. For the steady-state DC case, radial temperature results are obtained for arcs in nitrogen and sulphur hexafluoride at atmospheric pressure. It is shown that the inclusion of radiative self-absorption in sulphur hexafluoride arcs leads to a reduction in the centre temperature, a broadening of the temperature distributions and a small decrease in the axial electric field. Solutions are obtained also for the time-dependent behaviour of a nitrogen arc following an abrupt current interruption. In this transient case, self-induced radial flow is considered, leading to the additional process of convective loss.
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