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Heat2: 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:

Cylinder axisymmetric model

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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heat2_stud.zip

heat2.zip

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