Immersion depth and stem conduction

The sensing element of a probe sits some distance from the tip, and the stem connects it thermally to the outside world. If the probe is not immersed deeply enough, heat flows along the stem and the element does not reach the medium temperature. The error grows with the temperature difference between medium and ambient.

Checking it

Immerse to the working depth, record the reading, then immerse a further 20–30 mm and record again. A change indicates stem conduction; increase immersion until the reading is stable. Record the depth used for calibration and use the same in service.

Rules of thumb

• Immersion of at least ten to fifteen times the probe diameter plus the element length is a common starting point, but verify it.
• Short probes and dry blocks are the highest-risk combination.
• Insulating the exposed stem and the top of the block reduces the effect.

How big is the error, really

Stem conduction falls off roughly exponentially with immersion depth, which is why the advice is expressed in probe diameters rather than millimetres. A common working model is that the error is reduced by about a factor of e for every two to three diameters of additional immersion beyond the sensing element. That decay is fast, and it is why the difference between adequate and inadequate immersion is often a few centimetres.

A worked case makes the size of it obvious. A 6 mm probe calibrating at 100 °C in a room at 20 °C has an 80 °C driving difference. Immersed 40 mm — well under the usual guidance — a stem-conduction error of a few tenths of a degree is entirely ordinary. Immersed 120 mm the same probe may be inside a few millikelvin. Nothing about the sensor changed; only the depth did.

These come from the common rule of ten to fifteen diameters plus the element length. Treat them as the depth at which to start testing, not as a result. A thin-walled probe in a stirred bath will do better; a heavy sheathed probe in a dry block will do worse.

Why dry blocks are the hard case

A stirred liquid bath surrounds the probe with moving fluid that has high heat capacity and good contact, so the medium wins the argument with the stem. A dry block relies on conduction through an air gap between the probe and the well wall, which is a poor thermal path, and the block also has its own axial gradient — the top is cooler than the bottom because that is where the heat escapes. The two effects compound: the shallow part of the probe sits in the coolest part of the block and is also the part most strongly coupled to the room.

Practical mitigations: use the smallest well insert the probe will fit, fit an insulating plug or bushing at the block mouth, and where the manufacturer allows it, a little thermal paste or a snug insert to close the air gap. EURAMET cg-13 covers how to characterise the remaining axial and radial differences so they can enter the budget rather than be hoped away.

What to write down

• The immersion depth actually used, in millimetres, on the calibration record — not immersed fully, which means nothing to the next person.
• The result of the depth check: the reading at working depth and the reading 20–30 mm deeper, so a reader can see the residual.
• Whether the same depth is achievable in service. A probe calibrated at 150 mm and used in a 60 mm thermowell has been calibrated under conditions it will never meet.
• Any insulation, plug or insert used, since removing it changes the result.

The error always pushes the reading towards ambient. Above room temperature a shallow probe reads low; below room temperature it reads high. A calibration and a field use at different depths can therefore produce errors in opposite directions that partly cancel — which is luck, not control.