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A very long cylinder (infinite length) is maintained at temperature T_{i} along its internal surface and T_{o} along its external surface. The thermal conductivity of the cylinder is known to vary with temperature according to the linear function λ(T) = C_{0} + C_{1}·T.
Problem Type:
An axisymmetric problem of nonlinear heat transfer.
Geometry:
Given:
R_{i} = 5 mm, R_{o} = 10 mm;
T_{i} = 100°C, T_{o} = 0°C;
C_{0} = 50 W/K·m, C_{1} = 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.
Comparison of Results:
Radius, cm 
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 
See the Heat2.pbm problem in the Examples folder.