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This paper describes the first step toward a model of the liquid film at the rail/armature interface in solid armature railguns. It considers high- speed Couette flow with purely viscous heating and does not include MHD body forces or Joule heating. The focus is on coupled fluid dynamics and multi-phase heat transfer. The formulation is similar to the analysis of melt lubrication in rotating projectile bands, but our first principles model allows the possibility of solidification while the armature is passing, a feature that has been missing from previous analyses. The model is moderately successful at reproducing results of experiments which measured high-speed mechanical wear of 7075 aluminum sliding against ETP copper for face pressures ranging from 6 to 22 ksi. Discrepancies between calculated and experimental results are attributed to uncertainties in modeling the complex phase change behavior of aluminum alloy 7075 and uncertain conditions at the rail interface.