OK let me put the fluting thing to an end. Im an engineer and during school I payed extra attention to several structural problems I recognized were similar to the barrel fluting issue even though I knew the answer to this before those problems confirmed it.
Fluting a barrel makes it weaker than it originally was...How can you say removing material makes a straight piece of metal stronger.
Lets say we have two 20 inch barrels. Both weight the same amount . One is fluted. Its outside diameter is larger than the non fluted. The fluted will have more surface area than the non so it will cool better. The fluted will be stronger because more of its mass it located farther from the center of the barrel. This increases its moment of inertia "I". This is the easiest way to explain this. Lets say you have two pipes 10 foot long. one is 1 inch in diameter and the other is 1 foot. Both weight the same, so the smaller pipe has a very thick wall or lets even say its solid. The larger pipe has a thin wall. If you try to spin each, the larger pipe will be the hardes to start spinning. (It would also be the strongest as long as any bending force was applied evenly) The larger pipe could also handle more torque too. Thats why truck driveshafts are large and hollow instead of small and solid.
The maximum stress in any bending object happens on its outer surface. The stess at a certain distace from the center of an object "y" can be found as below. So if you make that distance the raduis of the barrel, y = radius.
"M" is the moment applied to a barrel. For here we will just say thats the force of some weight hanging on the end of each of our barrels.
Now every material has a certain amount of stress it can take before it bends to where it cant go back into shape. Think of a copper wire. You barely push on it, and it comes back. You push a little harder, and it stays bent. So if both barrels are of the same material, they will each bend when that stress level occurs and any part of each barrel. So we take the equation:
Stress = (M)x(y) / I
And solve it for "M", the maximum weight each barrel can take before it bends.
M = (Stress)x(I) / (y)
lets say the stress the material can take is 1000psi. and the radius (y) of the round barrel is 1/2 inch (.5 in). Lets say the round barrels moment of inertia is 10 in^4 (im too lazy to actually calculate it)
1000psi x 10in^4 / .5in = 20000 in lbs
The fluted barrel has of course the same strength, but its effective radius will be larger than the round barrel so lets say its 10% higher at .55 in. And since it has more mass near the outside radius, its inertia will be a much higher, so lets say 20% higher at I = 12in^4
1000psi x 12in^4 / .55 in = 21818 in lbs or about 180 ft lbs of torque.
So the fluted barrel is 1.09 times stronger than the non fluted barrel of the same weight.
Not much difference in stregth, but youll get a fair big more surface area to cool the barrel.