# Critical Thickness of Insulation

Critical Thickness of Insulation

Consider insulation around a circular pipe as shown in the Details section. The inner temperature of the pipe is fixed at =350K. The pipe length is taken equal to .

T

i

L=1m

The heat losses per unit length of the pipe are given by:

q

L

2π(-)

T

i

T

∞

ln

r

0

r

i

k

1

r

o

where =1cm is the radius of the pipe, is the radius of the insulation, =298K is the temperature of the convection environment, is the thermal conductivity of the insulation, and is the heat transfer coefficient of the convection environment.

r

i

r

o

T

∞

k

h

This Demonstration plots the heat losses per unit length of the pipe versus the dimensionless radius of the insulation, /.

r

o

r

i

For sufficiently small values of , heat loss may increase with the addition of insulation. This is a result of the increased surface area available for losses by convection.

h

There is a critical radius, shown by the red dot in the figure, above which heat losses start to decrease. This critical radius is obtained by setting =0. The magenta region gives the values of the dimensionless radius, /, where the insulation is effective in preventing heat losses. The heat loss for a pipe without insulation is shown by the cyan dot in the figure.

(q/L)

r

o

r

o

r

i