Significance of Critical Radius of Insulation

  • For most cylinders, \(r_{oc} < r_i\) and the critical radius is of no concern. When cooling smaller diameter cylinders, such as electrical wiring, the critical radius must be considered, but one need not worry about it in the design of most large process equipment.

  • If the radius (for cylindrical and spherical surfaces) is greater than the critical radius, any addition of insulation on the tube surface decreases the heat loss. But if the radius is less than the critical radius, as in small-diameter tubes, cables, or wires, the heat loss will increase continuously with the addition of insulation until the radius of the outer surface of the insulation equals the critical radius. The heat loss becomes maximum at the critical thickness of insulation and begins to decrease with the addition of insulation beyond the critical thickness.

  • We can choose a insulating material in such a way that, it’s \(r_{oc}\) is less than or equal to that of bare pipe pipe radius (\(r_i\)). By this way, any addition of insulation to the pipe will reduce the heat loss. Refer to Fig.(3).

  • Critical radius of insulation is a property of the insulating material and outside convection heat transfer coefficient. It is having significance only for radii smaller than about few cm.

  • On windy days, the external convection heat transfer coefficient is greater compared to calm days. Therefore critical radius of insulation will be greater on calm days (note: \(r_{oc}\propto 1/h\)).

  • If the insulation of a steam pipe is wetted, the thermal conductivity of the insulation increases, which in turn increases the critical radius. Then it is possible that with the resulting critical radius the heat loss from the pipe will become larger with wet insulation than with no insulation.

  • The value of the critical radius \(r_{oc}\) will be the largest when \(k\) is large and \(h\) is small.

  • Noting that the lowest value of \(h\) encountered in practice is about 5 W/(m\(^2\).K) for the case of natural convection of gases, and that the thermal conductivity of common insulating materials is 0.05 W/(m.K), the largest value of the critical radius we are likely to encounter is \(r_{oc}=k/h=0.05/5=0.01\) m = 10 mm. This value would be even smaller when the radiation effects are considered. The critical radius would be much less in forced convection, often less than 1 mm, because of much larger \(h\) values associated with forced convection. Therefore, we can insulate hot water or steam pipes freely without worrying about the possibility of increasing the heat transfer by insulating the pipes.

  • The radius of electric wires may be smaller than the critical radius. Therefore, the plastic electrical insulation may actually enhance the heat transfer from electric wires and thus keep their steady operating temperatures at lower and thus safer levels.