Spiral is nice but would it be superior to straight fluting?
I'm no expert or physicist either, we're just discussing fluting theory for fun.
I would argue you are wrong about the cooling properties. There's a formula to calculate cooling and the surface exposed to air is an important factor to it. By fluting a barrel you increase that surface, thereby accelerating cooling.
The quality of a heavy barrel is that it takes more shots to warm-up it's extra mass.
For example, let's suppose any barrel was to suffer an important accuracy decline at 80°c. A light barrel may reach that temperature after a string of 20 shots while it'd take 40 shots for the barrel twice heavier.
The fluted barrel with a mass in-between may shoot a 30 round string to reach the 80°c but will cool faster than the 2 others.
Now that assumed those string were shot at rate of fire too fast to allow any meaningful cooling.
There's a slower rate that would allow both the fluted barrel and the heavy barrel to shoot around 50 rounds before they reach the temperature threshold.
There's an even slower rate that would allow the fluted barrel to never overheat while the heavy barrel overheat after 100 rounds.
Slower the rate, more important becomes the other variables like the loads, temperature, wind, sun, etc.
To some extent, fluting also brings a structural advantage. A 10kg h-beam being stiffer than a 10kg rod of the same length and steel. So a 1kg fluted barrel will be stiffer than a 1kg straight barrel of the same material and lenght.
Assuming it's a smart design and not the fancy pineapple previously mentionned.
You bring up valid consideration. Which revolves around the objectice of what the barrel is required to do. What if we consider, even though the temperature threshold is reached at a rate of fire such that the straight and fluted is reached in 50 rounds, but rate of fire maintains for another 30 shots. Which one holds or consistently puts them closer to point of aim?
I would say if you took a 30" straight barrel, and took a 30" barrel and fluted it, the straight barrel is more rigid and will shoot more before accuracy decline.
If you were trying to meet a weight restriction but also achieve X barrel length, its hard to say whats better.... 30" fluted at X weight vs 30" straight at X weight.
Or remove the length requirement. 30" fluted, vs 25" straight, weight is equal.
Or, remove the weight requirement and go 30" straight vs 30" fluted.
Edit: if you remove the weight requirement, I'm showing up with a minimum 1.250" straight 30" barrel. So you make a 1.5" fluted 30".....I would show up with a 1.5" straight.
If a guy with a fluted barrel puts a shot clock on a string, the straight always keeps up and may even have an edge.
If a guy with a straight puts a shot clock on it, the flute falls behind.
And I do reckon the rate of fire would have to be extremely slow in order for a fluted barrel to out cool/out shoot a straight barrel. OR, rate of fire is a 5 round group then full cooldown. At that point, the propertys dont mean anything because either barrel never came close to a heat related accuracy decline.
And just incase we forgot... still in full theory mode here.