[pcm81]

If i have a shallow and wide U shape made from iron or steel (non-stainless) and i place magnet on the bottom of the U with south and north poles pointing towards the sides of the U (N/S axis paralel to bottom of the U, will the sides/tops become N/S poles of the overall geometry? In Z axis the shape is a straight extrusion with no material on the other sides

N?                            S?
 |                              |
  |                           |
   |      N==S        |

[Enthalpy]

The iron short-circuits the magnet, leaving little effect at the iron's tips.

What makes the short circuit imperfect:

• If the magnet is wide, powerful and the iron is thin, then iron saturates, and the excess of magnet flux passes where possible, for instance to the iron's tips.
• Iron or steel have a hysteresis loop: they resist the flux. So some little field strength is still available across the short-circuiting portion of the U to create a flux outside the portion.
• • The maximum value of that "coercive field" depends on the material and its thermal and mechanical treatment
    https://en.wikipedia.org/wiki/Coercivity
    this distinguishes "soft" from "hard" magnetic materials.
  • How much it retains at a given moment depends on its past magnetic history.
• Iron or steel have a finite permeability. Often less important than the two previous limits.
  https://en.wikipedia.org/wiki/Permeability_(electromagnetism)
  this depends on the present situation rather than the history, except that eddy currents create a reaction time.
• There are no clear conductors nor insulators for magnetic fields, as opposed to electric currents. Present ceramic and rare-earth magnets have a small permeability, so only the parts of the magnet closest to the iron are well shorted. Other parts must cross the thickness of the magnet or air to join the iron, and this costs A/m so a part of the flux still passes elsewhere.

All these reasons leave more or less flux outside the short circuit, including at the iron's tips, where to poles have the same sign as at the magnet.

[pcm81]

The iron short-circuits the magnet, leaving little effect at the iron's tips.

What makes the short circuit imperfect:

• If the magnet is wide, powerful and the iron is thin, then iron saturates, and the excess of magnet flux passes where possible, for instance to the iron's tips.
• Iron or steel have a hysteresis loop: they resist the flux. So some little field strength is still available across the short-circuiting portion of the U to create a flux outside the portion.
• • The maximum value of that "coercive field" depends on the material and its thermal and mechanical treatment
    https://en.wikipedia.org/wiki/Coercivity
    this distinguishes "soft" from "hard" magnetic materials.
  • How much it retains at a given moment depends on its past magnetic history.
• Iron or steel have a finite permeability. Often less important than the two previous limits.
  https://en.wikipedia.org/wiki/Permeability_(electromagnetism)
  this depends on the present situation rather than the history, except that eddy currents create a reaction time.
• There are no clear conductors nor insulators for magnetic fields, as opposed to electric currents. Present ceramic and rare-earth magnets have a small permeability, so only the parts of the magnet closest to the iron are well shorted. Other parts must cross the thickness of the magnet or air to join the iron, and this costs A/m so a part of the flux still passes elsewhere.

All these reasons leave more or less flux outside the short circuit, including at the iron's tips, where to poles have the same sign as at the magnet.

This kind of confirms what i was thinking and was hoping was not the case.
This field question deals with magnetic stirrer design. I posted a related question about dancing stir bar in another forum. This question was meant to be about mag flux specifically, hence new thread.
Here is how the actual inside of the stir plate looks like:
https://ibb.co/sPSGrnF

I am planning to replace the magnets and was trying to reverse engineer this design to figure out their polarity. I was thinking that the rare earth magnets are meant to be further away from heat source, while the steel "boat" is meant to carry magnetic flux up towards the plate.

Most of the time the "cheap" stirrers i see have a more trivial design of a non-ferrous bar and 2 magnets at the ends with opposite poles pointing towards the plate. This more trivial design however places magnets closest  to the hot plate, resulting in the magnets getting hot and reducing their lifespan. Which is why this "boat" design looks interesting.

[pcm81]

Using a small magnet i have confirmed that the polarity of the permanent magnets is indeed along the bottom of "the boat"

[Enthalpy]

Don't focus too much on the temperature hypothesis. The most sensitive SmCo have a guaranteed operating temperature of +250°C, others guarantee +550°C, wow. Thanks to the fan, they won't get that hot.

I don't really grasp the purpose of the design with magnets along the iron. Definitely less induction available at the tips. A hypothetical advantage is that some induction is available over all the radius, hence fitting smaller stirring bars too, and not just at the tips when the magnets are there. But for that goal, less bad designs would be easy. And if the stirring bar has the proper length, magnets at the tips stabilizes its position.

Anyway, if yo suppose that the magnets lost their strength (I bet they didn't), they are easy to buy and replace. Take any SmCo (there are only 2 big groups distinguished by their composition, take the highest Curie temperature) of proper size from eBay or elsewhere. Be careful with strong magnets: all knives away, all iron away, think before acting.