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Problem Description

The problem to be solved is a simple model consisting of 2 concentric cylinders. The model contains three thermal nodes, one of which is a constant temperature boundary node. The geometry for this problem is shown in the figure below. 

This problem requires RadTherm to match the analytical solution, because each cylinder is assigned only one radiation patch.  This is done in RadTherm by using patch generation with values large enough to produce only one patch per part.  Without use of one patch per part, a temperature gradient will appear on the outer cylinder.  This is more correct but does not match the hand calculations.

Geometry for the concentric cylinder problem

Cylinder 1 (inner)	Cylinder 2 (outer)
radius:  50 mm	radius:  100 mm
length:  200 mm	length:  200 mm
30 elements along length	30 elements along length
30 elements around	60 elements around

Model Conditions

Cylinder 1 (inner)	Cylinder 2 (outer)
emissivity:  0.8	emissivity:  0.2
assigned 726.85 °C temp	calculated temperature
	conductivity:  0 W/m-K

Environment:

• Constant temperature of 300 K [26.85 °C]
• Emissivity: 1.0

Simplifying assumptions:

• No exchange of energy by conduction
• The room surrounding the geometry is very large.

Objectives:

Predict the steady-state temperature of the outer cylinder and the total heat loss by the inner cylinder.

Analytical Solution

TAI Results

The convergence criteria was set to provide the maximum convergence.  The obtained temperature of the outer cylinder was 442.72°C which is extremely close to the 442.71°C analytical.  The TAI Q2 was 362.586W versus a 362.708W analytical value.  Finally, the TAI Q1 was 1746.47W versus the analytical 1753.67W.

Note: Test run by RES 3-2000 using versions 5.0.0.