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# Pipes and Cylinders - Conductive Heat Losses

## Conductive heat losses through cylinder or pipe walls.

### Uninsulated Cylinder or Pipe

Conductive heat loss through the wall of a cylinder or pipe can be expressed as

Q = 2 π L (ti - to) / [ln(r/ ri) / k]                              (1)

where

Q = heat transfer from cylinder or pipe (W, Btu/hr)

k = thermal conductivity of piping material (W/mK or W/m oC, Btu/(hr oF ft2/ft))

L = length of cylinder or pipe (m, ft)

π = pi = 3.14...

to = temperature outside pipe or cylinder (K or oC, oF)

ti = temperature inside pipe or cylinder (K or oC, oF)

ln = the natural logarithm

ro = cylinder or pipe outside radius (m, ft)

ri = cylinder or pipe inside radius (m, ft)

### Insulated Cylinder or Pipe

Conductive heat loss through an insulated cylinder or pipe can be expressed as

Q = 2 π L (ti - to) / [(ln(r/ ri) / k) + (ln(rs / ro) / ks)]                          (2)

where

rs = outside radius of insulation (m, ft)

ks = thermal conductivity of insulation material (W/mK or W/m oC, Btu/(hr oF ft2/ft))

Equation 2 with inside convective heat resistance can be expressed as

Q = 2 π L (ti - to) / [1 / (hc ri ) + (ln(r/ ri) / k) + (ln(rs / ro) / ks)]                          (3)

where

hc = convective heat transfer coefficient (W/m2K)

## Related Topics

• Thermodynamics - Thermodynamics of steam and condensate systems.
• Insulation - Heat transfer and heat loss from buildings and technical applications - heat transfer coefficients and insulation methods to reduce energy consumption.
• Heat Loss and Insulation - Heat loss from pipes, tubes and tanks - with and without insulation - foam, fiberglass, rockwool and more.

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Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

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