The model I made has some simplifying assumptions that make it really easy to solve. I looked at the thermal resistance of the conduction in comparison to the convection and decided that assuming there is no convection or radiation was a good assumption. The model is a lumped mass model, meaning that the extruder is split up into a bunch of little pieces. The extruder is sliced into disks along it's longitudinal axis. Each slice is given an effective inside diameter and outside diameter and material properties. Each mass is treated as a thermal resistance and connected in series. The extruder is treated as a constant temperature heat source and the cold end is treated as a constant temperature heat sink. This model requires some design judgment to determine if the results mean anything. Anyhow, if you want more details, let me know.
The results are a pretty good match to Nop Heads measurements. The model is split up into 1mm slices, but it could be split into much less. Really only one slice is needed for each part where the cross sectional area and material properties are the same because the convection is assumed to be zero.
I didn't do anything make my model fit Nop's data, it is just right out of the model. Just to mention the model also gives the same prediction for heat loss out of the end of the extruder.Now the reason for developing the model is to see what we might be able to do to predict what would happen if we made some changes in the design. Now if we look up the glass transition temperature for ABS, we can see that it is right about 100 degrees C. The glass transition temperature is the point where the plastic starts to deform under light loads, and just above that temp it might start sticking the the walls of the extruder.
Lets consider design changes to make the temperature go down below the glass temperature quickly. The following figure shows the results if the necked down portion's outside diameter where simply to be reduced to 3.8mm. I know that is a thin wall, but it is steel, it should still be plenty strong. As you can see the temperature fairly quickly heads below 100 degrees C. The predicted heat loss to the "heat sink" in this design is .85 watts. For simplicity this may be the best design, or something like it. However, it is not the best performance in terms of quick temperature drop and low heat dissipation.
Lets see what might happen if we used a design where the stainless steel is a constant diameter:
Here we see what we expected, a linear temperature distribution, that would lead to lots of sticking on the walls. Also the heat dissipated is about 1.75 watts. Not really the best design.Now we consider Nop's previous design. Lets pretend for a moment that no bolts are needed to connect the heater to heat sink portion. Just a PTFE tube 5mm OD, 3MM ID, 5mm long. Lets have a look see at what the distribution would look like:
Now, that is the kind of stuff we wanted to see. However, it should be noted that under these condition the assumption that convection is zero is no longer quite as valid. A more realistic curve would not be so abrupt and the aluminum portion would be a little warmer, I think... well not really. Anyhow, what this shows us it that if we have a short portion with very low conductivity then the temperature distribution will have a quite drop. Ok, by the way the heat dissipated in the design is .13 watts. Note that this is without the screws!. If we can just get rid of the low resistance of those screws!
Here is a design that nearly eliminates the heat flow in the screws. Just about any screw material would work, but stainless steel would be marginally better than others. The Insulation doesn't have to be PTFE, I have suggested drywall board and hard board before. I think you will get the point though. Let me know if you have any questions. I understand that Nop is currently working on insulating the extruder end, but I don't know about the heat sink end. Insulating both would reduce the heat flow, but I don't think that it will have a large impact on extrusion performance.
