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Adds structural rigidity to the barrel
How?
Weight reduction, I buy. Heat dissipation, maybe, but it will be marginal as the surface area increase can be pretty marginal depending on the amount and depth of the flute. Also, since it's the same material, it's going to take the same amount of time for the heat to move to the surface of the barrel, again, depth of flute may aid this marginally.
I am an average rifle shooter on the best day, are flutes going to turn me into an above average shooter? No, are they going to make my rifle lighter and easier to carry in the field? Yes, but before I start taking chucks out of my barrel to lose gun weight, I should work first on myself to lose "self weight."
Anytime you change the radius of a bend in the same piece of material it makes it harder to bend the material in that the material has to bend at many different rates all at the same time. Basic engineering.
case in point an I beam compared to a simple rod of the same mass.