# Cylinders and Pipes - Conductive Heat Losses

## Conductive heat losses through cylinder or pipe walls

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### Uninsulated Cylinder or Pipe

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

Q = 2 π k L (t_{i}- t_{o}) / ln(D_{o }/ D_{i}) (1)

where

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

k = thermal conductivity of material (W/mK or W/m^{o}C, Btu/(hr^{o}F ft^{2}/ft))

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

t_{o}= temperature outside pipe or cylinder (K or^{o}C,^{o}F)

t_{i}= temperature inside pipe or cylinder (K or^{o}C,^{o}F)

ln = the natural logarithm

D_{o}= cylinder or pipe outside diameter (m, ft)

D_{i}= cylinder or pipe inside diameter (m, ft)

### Insulated Cylinder or Pipe

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

* Q = π L (t_{i} - t_{o}) / ((r_{s} ln(D_{o }/ D_{i}) / 2 k) + (r_{s} ln(D_{s }/ D_{o}) / 2 k_{s})) (2)*

*where *

*D _{s} = outside diameter of insulation (m, ft) *

*k _{s} = thermal conductivity insulation (W/mK or W/m ^{o}C, Btu/(hr ^{o}F ft^{2}/ft))*

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