We present a detailed analysis of a hydrodynamic constitutive model recently applied to study the non-local viscosity of highly confined inhomogeneous fluids (Zhang et al 2004 J. Chem. Phys. 121 10778, Zhang et al 2005 J. Chem. Phys. 122 219901). This model makes the assumption that, for pore widths significantly greater than the width of the viscosity kernel, one can approximate the true inhomogeneous kernel with a homogeneous kernel. We test this assumption with a simple mathematical model that mimics the simulation scheme of Zhang et al. Our analysis shows that the assumption of a homogeneous non-local viscosity kernel is reasonable for low density fluids confined to relatively large pore widths (channel separation distances) but becomes less reliable for higher density fluids and smaller channel separations. We find that the extraction of the viscosity kernel is not simple because of the lack of information about the stress response function at the fluid–wall boundaries. This lack of information can lead to singularities in the kernel and can also distort its shape. As a concluding remark, we also suggest a methodology which avoids these problems.