# 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 =(t2 π L_{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)

= pi = 3.14...π

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)*