This paper proposes a detailed numerical model of a very narrow air gap of a permanent magnet synchronous machine without an imposed axial flow. The flow structure analysis and the convective heat transfer are carefully investigated using an axisymmetric model of two concentric cylinders where the inner cylinder is rotating and the outer cylinder is stationary. For the different cases, only isothermal boundary conditions have been considered. The impact of the air gap mean temperature and of the rotation speed are thoroughly studied and all numerical findings are compared with analytical dimensionless correlations. CFD simulations show the existence of two critical Taylor numbers corresponding to the onset of further instabilities into the air gap which matches with theoretical and experimental previous results found in the literature. The Nusselt number distribution given by CFD shows a disparity with the dimensionless correlations which underestimate the effective convective heat transfer in very narrow air gaps. The numerical simulations allow the definition of a piecewise expression able to fit well the overall Nusselt number distribution over a relatively large range of Taylor numbers up to 3×10 4 . The present work shows the contribution of CFD numerical methods on the estimation of convection thermal resistances in very narrow air gaps.