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Cylinder with temperature dependent conductivity

nonlinear thermal analysis, temperature dependent conductivity, temperature distribution in cylinder

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
Cylinder with temperature dependent conductivity Determine the temperature distribution in the cylinder Cylinder R1 R2 T1 = 100°C T0 = 0°C

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

Task
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:

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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