Non Newtonian to me indicates quite viscous, and you're talking about a tube, so the diameter is small. Flow will very likely be laminar, regardless of whether it's shear thinning or shear thickening. In laminar flow in tubes, the Nusselt number approaches a constant value for tubes which are long enough. In tube in tube exchangers, what ends up happening is that to a fairly close approximation, assuming the shell side does not limit and the shellside temperatures are close to constant, you get the same amount of heat transfer per unit length of tube, somewhat irrespective of the diameter of the tube. Increasing the tube diameter decreases the pressure drop and increases the area available for heat transfer, but because the Nusselt number is constant you don't get any benefit from that extra area- the film coefficient drops in inverse proportion to the area such that Q remains the same.