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.
How to calculate the effect of temperature-dependent thermal conductivity on the radial temperature distribution in a long cylinder?
Answer Typical applications Geometry
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Engineering question
Use an axisymmetric steady-state heat-transfer model with the specified nonlinear conductivity and compare the radial temperature profile with the analytical solution.
cylindrical thermal bodies, nonlinear conductivity materials, temperature-dependent conductors
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Simulation problem
Problem Type
Axisymmetric problem of heat transfer.
R1 = 5 mm, R2 = 10 mm;
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*.
The axial length of the model is arbitrarily chosen to be 1 mm.
Temperature distribution in a long cylinder:
* 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.
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