# Pipes and Cylinders - Conductive Heat Losses

### Uninsulated Cylinder or Pipe

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

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

where

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

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

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

π = pi = 3.14...

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

r_{o}= cylinder or pipe outside radius (m, ft)

r_{i}= 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 (t _{i} - t_{o}) / [(ln(r_{o }/ r_{i}) / k) + (ln(r_{s }/ r_{o}) / k_{s})] (2)*

*where *

*r _{s} = outside radius of insulation (m, ft) *

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

Equation *2* with inside convective heat resistance can be expressed as

*Q = 2 π L (t _{i} - t_{o}) / [1 / (h_{c} r_{i} ) + (ln(r_{o }/ r_{i}) / k) + (ln(r_{s }/ r_{o}) / k_{s})] (3)*

*where *

*h _{c} = convective heat transfer coefficient (W/m^{2}K)*

## Related Topics

### • Heat Loss and Insulation

Heat loss from pipes, tubes and tanks - with and without insulation - foam, fiberglass, rockwool and more.

### • Insulation

Heat transfer and heat loss from buildings and technical applications - heat transfer coefficients and insulation methods to reduce energy consumption.

### • Thermodynamics

Thermodynamics of steam and condensate systems.

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