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# Cylinder with temperature dependent conductivity

A very long cylinder (infinite length) is maintained at temperature Ti along its internal surface and To along its external surface. The thermal conductivity of the cylinder is known to vary with temperature according to the linear function λ(T) = C1 + C2·T.

Problem Type:
Axisymmetric problem of heat transfer.

Geometry:

Given:
R1 = 5 mm, R2 = 10 mm;
T1 = 100 °C, To = 0 °C;
C1 = 50 W/K·m, C2 = 0.5 W/K·m.

Problem:
Determine the temperature distribution in the cylinder.

Solution:
The axial length of the model is arbitrarily chosen to be 5 mm.

Results:
Temperature distribution in long cylinder:

 Radius (cm) Temperature ( °C ) QuickField Theory 0.6 79.2 79.2 0.7 59.5 59.6 0.8 40.2 40.2 0.9 20.7 20.8

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