New Reynolds equation for line contact based on the Carreau model modification by Bair

This paper presents a new form of the one-dimensional Reynolds equation for lubricants whose rheological behaviour follows a modified Carreau rheological model proposed by Bair. The results of the shear stress and flow rate obtained through a new Reynolds–Carreau equation are shown and compared with the results obtained by other researchers.

► We present a new analytical Reynolds–Carreau equation for line contact.
► Expressions for the mid-plane stress, velocity field and flow rate are provided.
► Analytical formulae presented are applicable to a wide range of conditions.
► Results show very good correlation with previous simulations of other authors.