We present an asymptotic study of steady two-dimensional radial flow between converging plane walls (Jeffery–Hamel flow) when the viscosity μ and density ρ vary with the angular coordinate θ. Two representative situations are considered, the first, being a two-layer system (in which μ and ρ are uniform except for discontinuities at an interface θ = θI), and the other involving a fluid for which μ and ρ vary continuously with θ. The flow is analysed in the asymptotic limit when a parameter c related to the wall pressure gradient is large; this corresponds to converging flow at large Reynolds number. Solutions are derived for the boundary layers at the walls and for the shear layer at the interface; the results are shown to agree well with some exact (numerical) profiles.

The solutions obtained are not unique, though for given c they represent the ‘simplest’ type of profile, and the one that seems most likely to be stable. We demonstrate the non-uniqueness by deriving in §3 an alternative solution for the interfacial shear layer. This solution, however, can exist for only restricted ranges of values of the density and viscosity ratios, and involves an outgoing jet, suggesting that it is likely to be unstable.