The shape may dissipate heat better, but that muzzle break looks like a real POS, and the machining at the crown looks down right crude.
looks like more surface area for better cooling, other than that who knows...
I would like to address the above two suggestions:
While this may seem the case, this is not the intent. Traditionally, proper
fluting of a heavy barrel is done for the purpose of lightening the weight of a barrel while allowing for much of the gains of a heavy barrel (temperature stablisation, harmonics etc). Traditional fluting does offer more surface area with concave scalloping and hence more surface area to dissipate to air.
In this case,
straight slabs are cut from the barrel. In fact the surface area is
decreased. The barrel may still in fact provide benefits of lighter weight but decreases surface area and metal for temperature control.
Without knowing the exact dimensions, take for example the following:
eg: A circular form with a radius r = 2 units
Circumference is therefore 2(pi)r = ~12.566 units
For simplicity sake, we'll divide the circle into 6 equal units.
Therefore the length of each unit's arc is also equal to ~2.0943 units
You may notice that by dividing the circle into 6 equal parts, you can make 6 equilateral triangles and therefore all sides = r = 2 units
Where the circle circumference is = 12.566 units,
Cutting 3 arcs from the circle leaving 2 unit length 'slab straight sides' leaves a circumference of 12.283 units.
[ New circumference of irregular = 12.566 - 3(2.0943) + 3(2) = 12.283 units]
(Equal 'pies' were used for simplicity of demonstration, you can make whatever pies you want but the straigh slab will always be less than the length of the natural arc)
So....
Looks cool but the barrel profile and muzzle brake are made as such to save production costs (rather than traditional fluting).
ie They went cheap.