Critical Thickness of Insulation

heat transfer coefficient

0.5

thermal conductivity

1.5

Consider insulation around a circular pipe as shown in the Details section. The inner temperature of the pipe is fixed at

T

i

=350K

. The pipe length is taken equal to

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

h

,

where

r

i

=1cm

is the radius of the pipe,

r

o

is the radius of the insulation,

T

∞

=298K

is the temperature of the convection environment,

k

is the thermal conductivity of the insulation, and

h

is the heat transfer coefficient of the convection environment.

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

h

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

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

(q/L)



r

o

=0

. The magenta region gives the values of the dimensionless radius,

r

o

/

r

i

, 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.