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By experimental observation we show that the plasma flow and heat transfer within a direct current (DC) non-transferred arc plasma torch always show appreciable three-dimensional (3D) peculiarity even when the geometricalconstruction of the torch and working gas admission and exteal electrical collection conditions are completely axisym-metrical. Previous two-dimensional (2D) modelling studies cannot predict the 3D peculiarity of the plasma torch. Wehave successfully performed 3D modelling, and in this paper we present the modelling results for the plasma flow andheat transfer characteristics in a laminar DC non-transferred arc argon plasma torch. The predicted arc-root locationon the surface of the torch anode and arc voltage compare favourably with the corresponding experimental results.