The study of 21cm line observations of atomic hydrogen allows detailed insight into the kinematics of spiral galaxies. We use sensitive high-resolution VLA data from The HI Nearby Galaxy Survey (THINGS) to search for radial gas flows primarily in the outer parts (up to $3times r_{25}$) of ten nearby spiral galaxies. Inflows are expected to replenish the gas reservoir and fuel star formation under the assumption that galaxies evolve approximately in steady state. We carry out a detailed investigation of existing tilted ring fitting schemes and discover systematics that can hamper their ability to detect signatures of radial flows. We develop a new Fourier decomposition scheme that fits for rotational and radial velocities and simultaneously determines position angle and inclination as a function of radius. Using synthetic velocity fields we show that our novel fitting scheme is less prone to such systematic errors and that it is well suited to detect radial inflows in disks. We apply our fitting scheme to ten THINGS galaxies and find clear indications of, at least partly previously unidentified, radial gas flows, in particular for NGC 2403 and NGC 3198 and to a lesser degree for NGC 7331, NGC 2903 and NGC 6946. The mass flow rates are of the same order but usually larger than the star formation rates. At least for these galaxies a scenario in which continuous mass accretion feeds star formation seems plausible. The other galaxies show a more complicated picture with either no clear inflow, outward motions or complex kinematic signatures.
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