Everyone is generally aware of the need for comparisons and that a comparison based on only one aspect of a problem may not be sufficient for characterization.
For example, every student has probably encountered a professor that he or she would consider arrogant. But it is plain that all of those so characterized are not equally arrogant. Surely an arrogance scale could be constructed but we know that our like or dislike of those professors cannot be based solely on their degree of arrogance.
The characterization of problems in conduction are not as complicated or subjective as characterizing the traits of human beings but the need for norms is apparent. For those who believe that a professor is not a human being, let me say that they could not be more wrong. Beneath that arrogant exterior usually lies a wonderful person who feeds birds in the park, enjoys hiking in the woods and drinks to excess alone.
We also note of use of scales in judging stocks in the Stock Market. When judging a particular stock for investment one uses a variety of scales. There is the 50 day moving average which judges the instantaneous value of that stock relative to it 50 day average back from it current value. One can also judge a stock relative to the S&P 500 average. In the former case, we see how the stock is performing against it past and in the latter case relative to a group of stocks characterizing one aspect of the stock market. There are other averages but investors know that scaling is important in making investment decisions and that the use of more than one scale is necessary before investing.
The conduction problems in this module involve a description in the form of a differential equation and boundary conditions. The dependent and independent variables of the ODE are scaled in terms of dimensionless variables and dimensionless parameters which characterize all aspects of that problem. Now for an example.