Last post we talked about the idea of a
“penetration depth” to describe how deeply a fluctuating surface temperature
might affect the temperature of the ground below.
Before we go on to talk more about the
ground, we should point out that that kind of calculation isn’t limited to just
temperature distribution in the ground.
It can be used to approximate the penetration depth of many situations
where the surface temperature fluctuates periodically. For example, if you wanted to estimate how
deeply the temperature fluctuations penetrate into the wall of an engine
cylinder, you might use properties for steel (α
=17.7 mm^2/s) and the frequency of the periodic temperature variation of the
cylinder (if the engine was running at 2000 rpm, you’d have 1000 temperature
cycles per minute, or a frequency of 105 rad/s). With those numbers, and using our definition of 2.2% fluctuation for the penetration from the last post, you could calculate a penetration
depth of 2.2 mm.
