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Multilayer coated pipe
A very long cylindrical coated pipe (infinite length) is maintained at temperature T_{inner} along its internal surface and T_{outer} along its external surface.
Problem Type:
Plane and axisymmetric problems of heat transfer.
Geometry:
Thin layer of 3 mm coating is placed between steel pipe and insulation.
Given:
T_{inner}= 85°C, T_{outer}=4°C;
Thermal conductivity of steel λ=40 W/K·m,
Thermal conductivity of coating λ=0.4 W/K·m,
Thermal conductivity of insulation λ=0.15 W/K·m.
Problem:
Derive heat flux at the internal diameter and calculate the overall heat transfer coefficient (OHTC) of the system.
Solution:
The OHTC of 3layered pipe can be calculated as
λ_{total} = 2πL / [ 1/λ_{1}·ln(r2/r1) + 1/λ_{2}·ln(r3/r2) + 1/λ_{3}·ln(r4/r3)],
where L is the length of the tube.
For very long pipe the heat transfer in axial direction may be neglected, thus the temperature distribution in any cross section will be the same. In this case the planeparallel can be solved. In planeparallel problems all integral values are calculated per 1 meter of depth.
Because, the axial length of the axisymmetric model do not affect to results, it was set to some small value (0.05 m) to reduce the mesh size. To convert heat flux (and other integral values) calculated in axisymmetric problem to flux calculated in planeparallel problem the former should be multiplied by 20.
Results
Temperature distribution in multilayer coated pipe:

QuickField 
Theory 
plane 
axisymmetric 
Heat Flux, W 
178.2 
8.89·20 = 177.8 
 
Temperature difference, K 
81 
81 
81 
OHTC, W/K·m 
2.200 
2.195 
2.211 
Reference
Heat transfer for Engineers  H.Y. Wong Table 2.2 with the heat transfer coefficient set at infinity
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