<p>The study here is of two-dimensional constricted channel flows and insight into their properties as the degree of constriction varies. This is potentially helpful for a range of applications as well as being of basic scientific interest. Two main computational approaches are taken, one via direct numerical simulation of the Navier-Stokes equations, and the other in the large Reynolds number limit where the boundary layer equations apply wall-to-wall. The focus is on understanding more of, and quantifying, the relatively unknown effects of wall icing in channel flow of water, as well as making quantitative comparisons between solutions from the two computational approaches and similar comparisons with recent work on the melting of wall-mounted ice. Flow separation, eddy lengths, pressure responses for sufficiently constricted internal vessels and upstream or downstream influence are examined. The retention of the ice when undercooling is present at the vessel wall is also studied. Severe blocking followed by eventual mild blocking or complete unblocking of the water flow is commonly found.</p>