• Calculate ideal insulation thickness of pipes and wires considering the concepts of critical thickness of insulation.

Adding insulation to a cylindrical piece or a spherical shell, insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates. For a cylinder, $r_{cr} = \dfrac{k_{\mathrm{insulation}}}{h_\infty}$ For a sphere, $r_{cr} = \dfrac{2k_{\mathrm{insulation}}}{h_\infty}$ where,
$r_{cr}$ = Critical radius of insulation
$h_\infty$ = Convection coefficient outside the pipe sufficiently away from the surface
Note that for most applications, the critical radius is so small. Thus, we can insulate hot water or steam pipes without worrying about the possibility of increasing the heat transfer by insulating the pipe.

Solved Example:

81-3-01

A steam pipe 10 cm ID, and 11 cm OD, is covered with an insulating substance (k= 1W/mK). The steam temperature and ambient temperature are 200$^{\circ}\mathrm{C}$ and 20$^{\circ}\mathrm{C}$. If the convective heat transfer coefficient between the insulation surface and air is 8 W/sq mK, find the critical radius of insulation.

Solution:
$\quad r_{cr} = \dfrac{k}{h}= \dfrac{1}{8}= 0.125\ m = 12.5\ cm$

Solved Example:

81-3-02

For pipes, the radius of the pipe is taken higher than the critical radius, so that any insulation added will ______. (UPRVUNL AE ME July 2021)