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# Simple 2-D Thermal Analysis

#### broomdust

##### New member
I'm having a problem modeling a simple 2-D heat transfer problem for a class I'm teaching. Most students in our program use Pro/E and Pro/Mechanica for their Mechanical Engineering projects, and for that reason I'd like to know how to work out the follwing using Pro/E:

My students were asked to use numerical analysis to determine the temperatures of a flat, 2-D plate four units square given temperatures of 0 deg C on three sides and 100 deg C on the fourth.

I would like to show a graphical representation of this to my class (and also explain to them how they can do such modeling in Pro/E themselves) but I can't seem to follow the right steps to set boundary conditions properly. Can anyone suggest how they would set this up in Pro/E? If I've forgotten anything Pro/E would need to do this, please let me know.

Pro/Mechanica will have trouble with this one as described, because your boundary conditions are inconsistent at the corners - you are specifying TWO temperatures at the one point (100 degrees and 0 degrees). Pro/M won't accept this inconsistency in boundary condition specification (i.e. infinite temperature gradient).

Conventional h-element FEA packages may appear to work with this same problem, but in reality, you are defining nodal temperatures at the discrete perimeter nodes, so while there is a sudden jump between the adjacent specified nodal temperatures, there is a small but finite distance between the adjacent nodes (the element side length), and the resulting temperature gradient is very high, but finite.

You will need to consider one of the following model definitions in Pro/M, depending on the nature of the problem you are really trying to solve:

a) Don't specify the temperature along the two sides that meet the 100 degree side, and let Pro/M work out the temperature profiles.

b) Specify the temperature profiles along these sides using a formula that gives a continuous temperature profile (no sudden discontinuity in specified temperatures).

c) Split these edges, allowing a short length of undefined temeprature for Pro/M to calculate, beween the 100 degree and 0 degree specifications.

Also, I think you will need to add a Heat Load somewhere in your model - I can't get Pro/M Thermal to run unless I specify both Heat Loads and Heat Boundary Conditions. (Other users may know how.) What I do is apply a very small heat load (0.000001 W/m2, say) to a minor edge of the mdoel.

Hope this helps.