First, let's clear up a misconception.
Shadows move faster at the beginning and end of the day
This is not true. The angle to the sun changes at a constant rate during the day. That rate is easy to calculate, since it's 360°/day = 15°/hour.
Shadows can appear to move faster or slower at different sun orientations (times of day) due to the geometry between the object casting the shadow and what it is casting the shadow on. For example, something sticking out from a west-facing vertical wall will have the fastest shadow as soon as the sun hits the wall around noon, and the slowest shadow right before the sun goes down.
What should the interval be for shadow movement during the middle of the day?
That all depends on what is fast enough to "show movement" in your context. There will be a difference between any two pictures taken with some time between. We can't know how much difference you consider "movement", and how much shadow movement translates to how much movement in the picture. If you're doing a macro shot of a flower, then a millimeter of shadow movement could be significant. If you are taking wide angle pictures of your back yard, it may take 10s of mm for a change to be noticeable.
Playback speed also matters. If you're going to show the pictures at 10 frames/second, you need 2.4 times the motion between pictures than if you were to show them at 24 frames/second.
It is better to say how long of a clip you want to show what length of real time. You then decide the playback frame rate, and the rest is just simple math.
For example, let's say you want 10 seconds of playback at 15 frames/second for every hour of real time. That 10 seconds will require 150 frames. Spread over an hour, that's a period of (1 hour)/(150 frames) = (3600 seconds)/(150 frames) = 24 seconds/frame.