My Best Example

What is the best illustration you use in class? While conversing with a faculty member at another educational institution, I asked him this question (answers to which sometimes trigger ideas for examples I can use in my classes or, at least, yield insight into what the other person considers important or his or her approach to teaching). The fact that this other educator was not an engineer made me that much more eager to hear his answer.

I don’t think he answered my question, but someone standing nearby asked the same question of me: “What is the best illustration you use in class?” I have many that could possibly qualify, but there is one of which I am most proud: the example about touching a hot object.

It was, I think, in fourth-grade science class that my teacher asked the class about why touching a metallic hot object feels so much hotter than touching a nonmetallic object at the same temperature. The answer, she said, was that metal conducts heat better than a nonmetal. And that was it. But the answer given to us was very unsatisfying to me. So metals conduct heat better, what did that have to do with anything? This problem stuck with me for many, many years until I was writing my book on transport processes, Biological Process Engineering: An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems. I decided to revisit my fourth-grade science problem to see what was really happening.

The more thorough answer to the problem involves a heat balance on the skin, including heat conducted to the skin by the hot object, heat carried away from the skin by conduction and convection, and thermoreceptors embedded in the skin providing the means of sensing temperature. I would not have expected a fourth-grade teacher to be able to explain all this to a class of eight or nine year olds, but it gave me a sense of closure to be able to finally understand the answer as a grown-up. Not only that, but, as an engineer, I was able to solve the problem numerically and demonstrate that the sensed temperature between touching the two objects really was different.

The numerical solution to the problem of touching a hot object is lengthier than can be included here, but it can be found on pages 395–398 of my Biological Process Engineering. You can look it up. In short, the problem is illustrated by Figure 1.

Figure 1: A representative heat conduction problem.

Figure 1: A representative heat conduction problem.

The steady-state heat balance on the finger at the point of contact between the object and the finger is

(heat conducted to the point through the object)

— (heat conducted from the point through the finger)

— (heat convected from the point by blood)

= 0.

Some assumptions had to be made about the depth of thermoreceptors in the skin (at the surface), the normal temperature of the skin and blood (28.6 °C), the temperature of the hot object (40 °C), and geometry (the finger was assumed to be a cylinder 13 mm in diameter). An aluminum object with a thermal conductivity of 206 N/(s ˚C) resulted in a calculated skin-surface temperature of 39.99 °C. A rubber object with a thermal conductivity of 0.15 N/(s ˚C) resulted in a calculated skin temperature of 33.8 °C. This difference becomes greater as the temperature of the hot object increases, so, at 100 °C, the perceived temperatures are 99.9 and 61.1 °C. This points to the inaccuracy of determining temperatures by feel. A lot depends on the internal properties of the object itself.

For my transport processes class students, this example may not have been anything special, but, for me, being able to answer a problem that had bugged me for years was a very satisfying triumph.