As I look for a new hunting rifle, I see that some have fluted barrels, such as the Mossberg Patriot for example and some do not.
What would the advantage of a fluted barrel be?
A fluted barrel has two advantages,
The flutes make the barrel lighter and thus easier to carry for long periods while hunting.
More surface area means that the barrel cools down faster. As barrels heat up they lose their accuracy to a degree. Normally while hunting this isn't a big deal, but when sighting in or practicing this needs to be taken into account.
Overall this seems to be more common on hunting rifles where a lighter rifle is easier to hunt with.