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Problem Description

A mild steel bar 100mm long is initially heated to 100°C steady state.  At time>0 the ends of the bar are changed to a constant 20°C.   This problem is a one-dimensional dynamic conduction problem.   Since the model is to be treated as one-dimensional, material thickness is not important.  (For reference, a thickness of 3 mm was used.)

The meshed bar is 100 elements long and 5 elements wide.  Since TAI software computes conductor lengths from the centroids of elements, the elements are made 1.0101mm in length to position the boundary element centroids at 0 and 100mm exactly.  To change the temperatures on the ends, the ends were assigned to two new parts.  These were assigned a temperature curve which was at 100°C at time zero and 20°C at time 1E-6 seconds.

Boundary Conditions

• The two ends are held at 20°C.

• At time=0 the entire bar is 100°C.

Assumptions

• Emissivity is set to zero (no radiation); the minimal software emissivity is slightly larger than zero.

• No convection

• One-dimensional

Objective

Predict the dynamic temperature gradient.

Analytical Solution

TAI Results

The simulation time step used was 0.025 minutes, and the convergence criteria was set to zero degrees temperature change and zero watts residual heat with a maximum of 1500 iterations.  Several snapshots of temperature distributions and an animation of the results are shown below.  Agreement between the theoretical and TAI results was very good and is detailed in the table below.

Animation info: start=0 min, end=3 min, 0.3 minute intervals.

Graph info: the solid lines represent the analytical prediction and the points represent the TAI results.

Element #	X Distance	Time	Analytical	RadTherm 5.0	WinTherm 5.0	MusesPro 5.0
353	70.71	60 sec	54.3	53.9	53.9	53.9
353	70.71	120	34.5	34.1	34.1	34.1
248	49.50	120	38.2	37.8	37.8	37.8
248	49.50	18	95.4	95.7	95.7	95.7

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