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# Natural convection from the horizontal tube surface

Horizontal steel tube, filled with the flowing hot water is surrounded by the still air.

Problem type:
Plane problem of the steady-state heat transfer.

Geometry:

Given:
inner diameter of the tube D1 = 120 mm,
outer diameter of the tube D2 = 140 mm,
temperature of the water Twater = 90°C,
temperature of the ambient air Tair = 20°C,
thermal conductivity of the tube λtube = 0.4 W/(m·K)

Calculate the temperature of the tube outer surface and the heat flux per meter of the tube length.

Solution:
Flowing through the tube water heats its internal surface up to the water temperature. Heat from the tube surface dissipates as a result of convection.
We estimate that the temperatures of the tube surfaces is equal to the temperature of the water:
Tsurface = Twater = 90°C.
This value is used for the convection coefficient calculation*:
α = 6 W/(m2·K).

Result:
Tube surface temperature: T = 80 °C.
Heat flux per meter of pipe length: F = 159 W.

*Remark: the formulas of the similarity theory gives the average value of the convection coefficient. This approach is very approximate by its nature, so there is no reason to make iterations to calculate the accurate Nusselt number related to actual surfaces temperatures.

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