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

where

hc = convective heat transfer coefficient (W/m2K)

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