Let's make some plots to show how it behaves.  First the inside fluid is twice as viscous as the outside fluid. M=2

Now M=10

Now M=100

If you were worried, we can check to see if M=1, if the profile looks correct, it does

Finally we could envision the reverse case, the outside fluid is more viscous.  We don't want to use this pump our fluid, but we might be interested to see what it looks like. M=.1

We can make this last case extreme to where the outside fluid is almost a solid pipe.  We would not consider a real flow like this but this kind of limit is often useful to check answers or help our conceptual thinking. M=.001