The main purpose of fluting is to reduce weight, and to a lesser extent increase rigidity for a given total weight or increase surface area to make the barrels less susceptible for overheating for a given total weight. However, for a given diameter, while a fluted barrel may cool more quickly, a non-fluted barrel will be stiffer and be able to absorb a larger amount of total heat at the price of additional total weight.
what is the benefit of a fluted barrel
to reduce weight increase rigidity for a given total weight