Bearcat, check out John Krieger's web site: www.kriegerbarrels.com
Go to the link/section on fluting. Note carefully what he says.
There is a lot of words (spoken and in print) saying that fluting a barrel makes it stiffer. But that's physically impossible. Here's why.
A barrel resists bending down by the force of gravity acting on it by how much material it has to resist bending. The thicker a barrel is for a given caliber and length the less it will bend. A 30-inch long 25 caliber barrel 1 inch in diameter held horizontally at one end will bend less than one of the same length and caliber only 3/8ths inch outside diameter. The reason the thicker barrel bends less is there is more material resisting compression (bottom of the barrel) and expansion (top of the barrel) in line with the force of gravity.
Holding a yardstick horizontally at one end demonstrates the same thing. With the yardstick's width vertical it won't bend much at all; hold the yardstick's width horizontal and it bends quite a bit. Again, it depends how much material resists compression and expansion in the bending force axis which is gravity. Take this yardstick and reduce its width to half, then retest. Retest again with its width reduced to equal its thickness and note how much it bends.
Anytime material is removed from the outside of a barrel there is less material left to resist bending. That's grade school physics. Any respectable mechanical engineer knows this. It doesn't matter if material is uniformly removed (reducing the outside diameter) or in lengthwise strips (fluting); there will be less material to resist bending after it's removed.
Those claiming that fluting a barrel will make it stiffer are wrong. When someone says fluting a barrel makes it stiffer, mention that some of the barrel material that resists bending has been removed. Then ask 'em why they think it would be stiffer as there's less material to resist bending.
As John Krieger says in his web site's section on fluting, a fluted barrel of the same caliber and weight per inch as a solid one a bit smaller in diameter will be stiffer. How much stiffer depends on how deep the flutes are and the outside diameters of both barrels.
A barrel with lots of deep flutes may cool a bit faster than a plain one. Someone did some tests years ago and found out a coarse bead blasted barrel cooled faster. What the cooling rate was didn't matter much as accuracy didn't suffer at all as long as the round didn't stay in the chamber more than 10 to 15 seconds before it was fired.