At 60 L/min water flowing in an open 50 mm diameter round channel, you're already well into the turbulent flow regime. Assuming that the liquid film coefficient remains the controlling heat transfer resistance, your optimal rod diameter will be the one which gives the maximum pressure drop you can provide. At a certain point, though, the thermal conductivity of the thing with the 50 mm hole in it will come into play and you'll get diminishing returns.
If you want to do the math, here are the equations:
Nu = h D(hydraulic)/k
where h is the liquid film coefficient, a heat transfer CONDUCTANCE (i.e. bigger h means less heat transfer resistance). k is the thermal conductivity of water.
Nu = 0.023 Re^0.8 Pr ^0.3
D(hydraulic) = cross sectional area / wetted perimeter for your annulus, ie. (D^2-d^2)/(D+d) where D is 50 mm and d is the diameter of the rod
Re = D(hydraulic) V mu/k, where mu and k are fluid properties (i.e. constant for your situation) and V is the velocity of the flow
Pr is a function of fluid properties only (i.e. it's constant for your situation).
From this you could derive the dependence of h on D (50mm) and d (the diameter of the inner rod). All that matters for you, though, is that there is no optimum annulus- the smaller the annulus, the greater the heat transfer at a given mass flow- and the (vastly) greater the pressure drop too.
Practical considerations, such as how much pressure you can reasonably supply to force 60 L/min through this hole, and how much this pressure will increase with scaling, and how much erosion/corrosion you get at high velocities, will determine what the REAL optimum annular space would be.
As to using turbulators, static mixers or enhanced roughness rather than a rod in the ID, I doubt they'd make that much more effective use of available pressure drop for beneficial radial mixing in your situation than would be afforded by a simple rod, since your flow conditions are fully developed turbulent even without the rod in place. They'd make a world of difference if your flow was laminar, though!