  Wall slip and wall divergence are known to have large and opposing effects on
the stability of flow in a two-dimensional channel. While divergence hugely
destabilises, slip dramatically stabilizes the linear mode. In a non-parallel
stability analysis, we study a combination of these two effects, since both
will coexist in small-scale flows with wall roughness. Our main results are (i)
that the stabilising effect of slip is reversed at higher angles of divergence,
(ii) transient growth of disturbances is unaffected by either wall-divergence,
or by slip at any divergence. Moreover, at the Reynolds numbers relevant here,
transient growth is too low to be a significant player in transition to
turbulence, which is more likely to be driven by linear instability.
