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Heat2: Cylinder with temperature dependent conductivity
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_{1} + C_{2}·T.
Problem Type:
Axisymmetric problem of heat transfer.
Geometry:
Given:
R1 = 5 mm, R2 = 10 mm;
T_{1} = 100 °C, T_{o} = 0 °C;
C_{1} = 50 W/K·m, C_{2} = 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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