Critical
radius of insulation: Heat loss from an insulated pipe varies as radius of
insulation. Heat loss is minimum at
critical radius. The thickness of
insulation corresponding to critical radius of insulation is known as critical
insulation thickness. If we insulate
beyond this point, heat loss rate increases.
This radius at critical heat loss is given as
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Example
5.3: Find the critical radius of insulation for a
pipe surrounded by asbestos and exposed to air. Determine the heat loss from the pipe at 527 °F for the
following cases: (1) pipe without
insulation; (2) pipe with insulation thickness same as the critical thickness;
(3) with insulation thickness 0.049 ft more than the critical thickness; and
(4) with insulation thickness 0.049 ft less than the critical thickness. Given the following data:
Outside radius
of the pipe, ro = 0.082 ft,
Ambient
temperature, Ta = 50 °F,
Convective
heat transfer coefficient, hc = 0.616 Btu/(hr·ft2·°F);
Thermal
conductivity of insulation, k = 0.105 Btu/(hr·ft·°F);
Solution: The critical radius of insulation, rc
= k/h = 0.17 ft. Surface
temperature, Ts, is 527 °F, whereas the ambient temperature, Ta, is
50 °F. The heat flow rate, q, is given as
|
where
r2 is the insulation radius and L is the pipe length.
(1)
Without insulation, r2 = r1 = 0.082 ft:
$
Resistance from convection term
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(2)
With pipe having insulation thickness represented by the critical insulation,
r2 = 0.17 ft:
$
Total resistance is a combination of conductive and
convective terms.
|
$
Heat loss, q2 = 181.72 Btu/hr.
(3)
With pipe having insulation thickness 0.049 ft greater than critical radius:
r3 = rc
+ 0.049' = 0.219 ft
$
Resistance, R3 = 2.67 (hr·°F)/Btu,
$
Heat loss, q3 = 178.7 Btu/hr.
(4)
With pipe having insulation thickness 0.049 ft less than critical radius:
r4 = rc - 0.049' = 0.121 ft
$
Resistance, R4 = 2.72 (hr·°F)/Btu,
$
Heat loss, q4 = 175.2 Btu/hr.
It
can be seen that if outside radius of the pipe is smaller than the critical
radius of the insulation, one does not have to insulate to save heat loss. But we do not want to leave hot pipes bare
for safety reasons.