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Heating Up, But Slowly

Last week we talked about that mug of coffee and the notion of thermal capacitance. Thermal persistence is another way to think of this concept.

To one degree or another things are slow to change temperature. This is due to both the way heat is transferred (convection is rapid while conduction tends to be slower)and the amount of heat needed to cause that change. An obvious example is that a great deal of energy is involved when water changes temperature compared to air changing temperature.

If we drink the hot coffee quickly, the mug remains warm.
Over time the mug begins to cool as its heat transfers to the surrounding air
As more time passes the mug cools even more. Eventually it will reach a “steady-state” temperature in relationship to the ambient surroundings.

The coffee mug was slow to heat up. We could see that in the three time lapse images below. The heat from the very hot coffee transferred into the cooler mug. In time, the coffee cooled enough that it is drinkable and the mug warmed enough to feel quite pleasant. These relationships are the first half of a cycle of transient heat transfer.

When we drink the coffee completely, the second half of the cycle begins. The air in the mug quickly cools toward the ambient air temperature. The mug now begins transferring heat to the air in the mug and around it. Notice how long the mug remains warm compared to our hands. The heat in the ceramic is slow to move (by conduction) and there is quite a bit of it to move.

We need to be careful whenever we look at materials we are working with. Whether it is the wall of a house or an overhead line, we need tounderstand whether or not they are in a transient state, and if  they are warming up or cooling down. If the sun has begun to shine on a south-facing wall, for example, when will that heat show up on the inside? If the load has recently decreased on a breaker, how long will it be before the circuit cools to a new steady-state temperature?

Failing to take these simple relationships into account means we will make mistakes in our analysis. These could simply be a valuable learning experience or they could be quite costly. In either case it is important to pay attention to both thermal capacitance and transient heat flow.

Thinking Thermally,

John Snell—The Snell Group, a Fluke Thermal Imaging Blog content partner

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