Thermal Expansion, Friend Or Foe?

Thermal Expansion is the propensity of solid matter to increase its volume when heated. This change in volume occurs in all directions of an object in length, width, and height. The amount of change is proportional to the change in temperature, the initial dimensions of the object and by material itself. Thermal expansion can work with you or against you, depending on the how objects are arranged.

First, here are a few interesting examples of thermal expansion. The truss of the Eiffel Tower is made of iron and stands 1063 ft tall. The temperature in Paris varies through the year from about 30 to 80°F or a 50°F temperature swing. On hot days, the tower is 6" taller than on cold days.

Railroad tracks are made of hot rolled medium carbon steel. Depending on where they're located in the world, track might see a large temperature swing over a year, possibly as much as 80°F. Between those temperatures a mile of track varies in length by as much as 30" or almost 2 1/2 feet between winter and summer. That expansion and contraction must be account for in track layout to avoid warping and bucking of the tracks which can lead to train derailment.

Let’s get into it:
The amount of growth or an object is calculated by only having to know 3 things and multiplying them together. They are the starting dimension from where you want to measure your expansion (or contraction), the change in temperature (in °F in our examples), and the coefficient of thermal expansion (CTE) for the material (in imperial units). You can find CTEs online with a simple search, but here are a few common ones.

The prefix µ is the Greek letter mu, meaning micro or millionth.
Glass and polyethylene are included in the list to show how varied different thermal expansion rates can be.

Here's how to perform some calculations.
Imagine you have a cylindrical cartridge heater measuring 24" long, and you want to know how much it will elongate if it goes from 72°F to 1000°F. The cartridge heater sheath is made of Incoloy 800. The CTE of Incoloy 800 is 8.0 µin/in·°F. That elongation factor is read as 8 millionths of an inch per inch in length per degree Fahrenheit.

Knowing those three values and multiplying them together gives you:
24in x (1000°F-72°F) x 8.0 µin/in·°F.

Written without the units to make it easier to read you have:
24 x (1000-72) x 0.000008 = 0.178".
The heater will elongate by almost 3/16". That difference is easily measured with a tape measure.

The same calculation can be performed for the diameter of the heater. If you're told the heater has a diameter of 0.620" at room temperature, then its size at temperature is calculated as follows:
0.620 x (1000-72) x 0.000008 = 0.0046". The heater will increase in diameter by almost 0.005".

When the heater gets hot it should enlarge to snuggly fit in the hole it's inserted into.

There is a slight downside to this. Just as the diameter of the heater gets bigger, the hole that its inserted into gets bigger too. Fortunately, the walls of the hole do not get as hot as the heater itself, so the hole expansion will be less than the heater. Additionally, if the block that the hole is in is made of plain steel, the expansion will be less still because the thermal expansion rate of plain steel is less than that of Incoloy 800.

Let's assume the wall of the hole in the plain steel block only reaches a temperature of 800°F, that means the hole expansion, going from 0.625", would be 0.625 x (800-72) x 0.000006 = 0.0027”.

That means the hole would enlarge from 0.625" to 0.628" and the heater would enlarge from 0.620" to 0.625". There would be a smaller gap between the heater and hole than when you started, meaning a better fit and better heat transfer.

With band heaters, it's a similar affair, except the hotter object is the heater on the outside and the cooler object is what's being heated, on the inside. Unfortunately, that means that band heaters get loose when they're heated. No matter how much they're originally tightened at room temperature they'll always get loose.

Here's why. A 6” diameter band heater (let’s say), made of stainless steel and heated up to 800°F enlarges in diameter by this much: 6 x (800-72) x .000008 = 0.035".

The barrel that the heater is mounted to is made of plain steel (in this example) and experiences a temperature of 600°F. That means it expands in diameter like this: 6 x (600-72) x .000006 = 0.019".
It’s easy to see with these simple calculations that the heater expands more in diameter than the barrel, allowing the heater to become loose.

That's why it is so important to retighten band heaters when they're as close to operating temperature as possible, as long as it can be done safely. Conveniently, Tutco does provide a spring bolt clamping option that helps with that issue by having a positive force constantly pulling the heater closed with a heavy-duty spring that’s incorporated into the clamping mechanism.

As you can see, thermal expansion can play an important factor when it comes to fitting your heaters to your application. Depending on the temperatures operated at, the materials used, and the size of your components affect how well the conduction between components is enhanced or can be made worse.