As most people who've had any elementary heat transfer course are aware, when insulating a pipe, wire, etc, there is a critical thickness for the insulation below which it causes greater heat transfer than no insulation would. In actuality, since the critical radius is a minimum, one needs to go even farther before it catches up to the uninsulated case. This effect is due to the thermal resistance from the added insulation (a function of material and thickness) being less than the decrease in thermal resistance to convection brought about by the increased surface area due to the thicker insulation. A more detailed explanation is found here
What I wonder is how large this critical thickness typically is for realistic cases such as an electrical wire, a steam pipe, or a water pipe (all cases in STP air)? I realize exact answers aren't possible given the fact that it will vary with material type, temperature diff., and size.
The motivation for this is that it theoretically could prevent wasting insulation or provide a practical avenue for energy dissipation, but Fundamentals of Heat and Mass Transfer 6e by Incropera et al. indicates that the effect is usually too small to be of practical importance.