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# Cylinder with temperature dependent conductivity

QuickField simulation example

A very long cylinder (infinite length) is maintained at temperature T1 along its internal surface and T2 along its external surface. The thermal conductivity of the cylinder varies with temperature.

Problem Type
Axisymmetric problem of heat transfer.

Geometry
R1 = 5 mm, R2 = 10 mm;

Given
T1 = 100 °C, T2 = 0 °C;
Thermal conductivity λ(T) = 50 + 0.5·T.

Determine the temperature distribution in the cylinder and compare with analytical solution*.

Solution
The axial length of the model is arbitrarily chosen to be 1 mm.

Results
Temperature distribution in a long cylinder: Reference
* A Heat Transfer Textbook, 5th ed. John H. Lienhard IV, University of Houston John H. Lienhard V, Massachusetts Institute of Technology. Example 2.4. Radial Heat Conduction in a Tube. 