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Abstract The Neutral Beam Test Facility (NBTF) in Padua, Italy, makes use of large ion sources based on the inductive coupling of radio-frequency (RF) waves with the plasma. Transport modelling provides tools to interpret and guide the experiments towards an efficient plasma heating and control. Although there exist comprehensive 2D fluid transport models assuming axial symmetry, some important features of these large ion sources are intrinsically three-dimensional. Here we present the first 3D numerical calculations, NBTF relevant, of a fluid transport model for the plasma electron density and temperature assuming ambipolar fluxes. The induced plasma current distribution driven by the RF current is evaluated with frequent updates of the absorbed power consistently with the evolving electron density and temperature distributions. Despite the simplicity of the transport model, it shows overall results in fair agreement with the present experimental knowledge. We present scans of the RF power fed to the driver at varying neutral gas pressure and temperature, and driving frequency. First results in presence of a traverse magnetic filter field, a clearly non-axisymmetric ingredient, indicate that previous 2D calculations considering the field either parallel or perpendicular to the calculation domain give acceptable limit cases. All these results set the basis for further studies aimed at helping in the operation and final design of the NBTF devices, which are the pilot plants for the ITER neutral-beam injection system.