Pipes and Cylinders - Conductive Heat Loss

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^oC, Btu/(hr ^oF ft²/ft))

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

π = pi = 3.14...

t_o = temperature outside pipe or cylinder (K or ^oC, ^oF)

t_i = temperature inside pipe or cylinder (K or ^oC, ^oF)

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^oC, Btu/(hr ^oF ft²/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/m²K)