Heat3: Multi-layer 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:

A plane parallel and axisymmetric problems of linear heat transfer.

Geometry:

Multi-layer coated pipe

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 3-layered pipe can be calculated as
λ_total = 2πL / [ 1/λ₁·ln(r2/r1) + 1/λ₂·ln(r3/r2) + 1/λ₃·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 plane-parallel can be solved. In plane-parallel problems all integral values are calculated per 1 meter of depth.
Becase, the axial length of the axysimmetrical 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 othe integral values) calculated in axisymmetric problem to flux calculated in plane-parallel problem the former should be multiplied by 20.

Results

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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