Hints, Tips and Solutions

Q:  Which model for thermal resistivity should I choose?  How good is the default model?

A:  There are four models with user adjustible parameters which can be used - a constant model (tcon.const), a power law model (tcon.pow), a polynomial law model (tcon.poly) and a reciprocal law model (tcon.recip).  The default is the compositionally dependent thermal conductivity model (tcon.comp), which is a version of the power model (tcon.pow) for which there are default parameters for certain popular materials.  

Here is a dem onstration of how to compare a model with experimental data.  The CRC handbook has a table of thermal resistivity vs temperature for silicon.  The data can be put into the TonyPlot data format, which will look like this:

This file will give you a graph of k versus T in TonyPlot.  After you have done that, the next step is to define the model function in TonyPlot.  We will be using the power law model, so the function definition will look like this:

To plot this in a way that we can see the model clearly,  we will be plotting the log of k versus the log of T,  so the model will appear as a straight line.  The display setup will look like this:

The TonyPlot shows the CRC data in red and the model (function 1) in green:

The fit of the power model to the data near room temperature is pretty good.  The black line is a fit to the curve in the region from 200K to 400K, which gives a slightly better fit.

 

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