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 (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)
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