The Delta-T That Somebody Added Thirty-Two To

Why this matters

Imported equipment arrives with manuals written in Celsius, and the number a tech most needs from them is usually a temperature difference: a rise across a heat exchanger, a drop across a coil, a supply-to-return split. Converting that difference the way you convert a thermometer reading, times 1.8 plus 32, makes the spec about 32 F bigger than it should be. On a small rise that is enough to make a healthy unit look like it is doing a third of its job.

This case is a tech who did exactly that on a plate heat exchanger and came within one phone call of quoting a replacement. It is worth following in detail, because the conversion slip was obvious once spoken out loud and the reasoning that would have caught it without anyone's help uses only the readings already on the ticket.

The call

A small commercial building heats its radiant floor through a plate heat exchanger, a stack of thin stamped plates that pass the boiler water on one side and the floor loop water on the other without mixing them. The unit was imported, packaged with its own pumps and controls, and its manual is metric throughout. The complaint was that the floor felt slow to warm up on cold mornings.

The tech clamped surface thermometers on all four connections after the system had been running steadily for half an hour:

• Floor loop (secondary) entering the exchanger: 95 F. Leaving: 113 F. Rise: 113 - 95 = 18 F.
• Boiler loop (primary) entering: 150 F. Leaving: 122 F. Drop: 150 - 122 = 28 F.

The manual's commissioning table gave a design temperature rise on the secondary of 10 C at rated flow. The tech converted it on his phone's calculator: 10 x 1.8 + 32 = 50 F. Against 50 F, an 18 F rise is 18 / 50 = 36 percent of design. The obvious reading was a scaled or fouled exchanger, plates coated on the water side so heat could not get through. He started writing the replacement up and called his supervisor to ask about lead time on the part.

The conversation

TECH: Plate HX on the radiant job. Manual wants a
      10 C rise on the floor side. That's 50 F. I'm
      getting 18. It's scaled up, I'm quoting a new
      exchanger.
SUPERVISOR: How'd you get 50?
TECH: Ten times 1.8, plus 32.
SUPERVISOR: That turns 10 C into a temperature.
      What's the manual giving you, a temperature or
      a rise?
TECH: A rise.
SUPERVISOR: Then the 32 doesn't belong. A rise is a
      difference, and the 32 cancels out of any
      difference. 10 C of rise is 18 F of rise.
TECH: So I'm at design.
SUPERVISOR: On that side. What's the boiler side
      doing, and what does the manual want there?
TECH: 28 F drop. Manual says 15 K.
SUPERVISOR: 15 K is 15 C of difference, 27 F. You're
      at design on both sides. Don't order anything.

Why the 32 does not belong

A Fahrenheit reading is 1.8 times the Celsius reading plus 32, because the two scales have different zero points: water freezes at 0 C and at 32 F. The 32 is the gap between the zeros.

A difference does not have a zero point. Take two temperatures in Celsius, convert each, and subtract:

• 45 C x 1.8 + 32 = 113 F.
• 35 C x 1.8 + 32 = 95 F.
• 113 F - 95 F = 18 F, and 45 C - 35 C = 10 C.

The 32 went into both readings and came out in the subtraction, leaving 10 x 1.8 = 18. That holds for every difference, so the rule is short: a temperature difference converts by 1.8 alone, in either direction. Multiply a Celsius difference by 1.8 to get Fahrenheit, divide a Fahrenheit difference by 1.8 to get Celsius, and never add or subtract 32. Temperature Conversion and the Delta-T Rule owns the full conversion set.

European manuals often write a difference in kelvin, as this one did for the primary side: "15 K". A kelvin is the same size as a Celsius degree, so 15 K of difference is 15 C of difference and 15 x 1.8 = 27 F. A manual that writes "K" is telling you plainly it means a difference, which is the cue the tech's secondary-side spec did not give him.

The hypotheses, and what each reading said about them

The supervisor settled the conversion in one question. What he did next is the part a tech can do alone, without a supervisor on the phone: check whether the readings themselves support the diagnosis, independent of any spec.

A fouled exchanger. Scale on the plates adds resistance to heat flow, so with the same two flows, less heat crosses. Less heat crossing means both sides change temperature less: the floor water rises less and the boiler water drops less. A fouled exchanger would show both the secondary rise and the primary drop short of design, together. Here the secondary rise was 18 F against an 18 F design, and the primary drop 28 F against 27 F. Both on design. That rules out fouling as the cause of the complaint, whatever the plates look like inside.

A thermometer error. Surface thermometers clamped on pipe read a little under the water temperature, more so on uninsulated or painted pipe. But the tech used one instrument model on all four points, so a fixed offset common to both readings on a side cancels in that side's difference. A spread between two different instruments would not cancel the same way, and is worth checking with one instrument moved from point to point. Here, the rise and drop both landing on design is itself evidence the readings are sound, because a random instrument error would not usually hit both specs.

Too much flow on the floor side. At a fixed heat input, more flow through the secondary gives a smaller rise. That would show as a rise below design with the primary drop normal. The rise was on design, so the floor loop's flow was where the manual expected it.

With the exchanger transferring design heat, the slow morning warm-up had to come from somewhere else. It turned out to be a control setting: the building's night setback had been widened at some point, so on a cold morning the slab started further below setpoint than the system was sized to recover from in the time allowed. A radiant slab responds slowly by nature. Narrowing the setback fixed the complaint. Nothing got replaced.

The spec that could not have been true

There was a third way to catch it, and it needs no manual at all beyond the flow. Heat carried by water is, in the US field form, 500 x gallons per minute x temperature difference in F, giving BTU per hour, where the 500 assumes plain water near 60 F (the derivation is in The Sensible Heat Formulas for Air and Water). The manual listed the secondary's rated flow at 20 liters per minute for this example, which is 20 x 0.264 = 5.28 gal per minute.

• At the real design rise: 500 x 5.28 x 18 = 47,520 BTU/h.
• At the tech's converted rise: 500 x 5.28 x 50 = 132,000 BTU/h.

The boiler feeding the exchanger was rated at 80,000 BTU/h input. No exchanger can hand the floor 132,000 BTU/h from a boiler that burns 80,000, so a 50 F design rise at that flow was not a spec the system could ever have met. A number that implies more heat out than the burner puts in is wrong before anyone looks at a plate. The 18 F figure, at 47,520 BTU/h, sits comfortably inside what the boiler can deliver.

What the slip would have cost

Had the quote gone out, the shop would have sold the customer a new exchanger, a day of draining, swapping and refilling, and a re-commissioning. The new exchanger would have produced the same 18 F rise, because the old one was producing design rise already, and the floor would still have been slow on cold mornings, because the cause was a setback. The callback would have arrived with a large invoice already attached to the wrong diagnosis, and the next tech would have started by distrusting a brand-new part.

The check that catches it without a supervisor

Convert the readings, not the spec. Take the four field readings and put them into Celsius one at a time, each with the full formula, because each one is a temperature:

• 95 F: (95 - 32) / 1.8 = 63 / 1.8 = 35 C.
• 113 F: (113 - 32) / 1.8 = 81 / 1.8 = 45 C.
• Rise: 45 - 35 = 10 C. Design: 10 C.

Done this way the 32 appears only where it belongs, on single readings, and the comparison happens in the manual's own units. It also catches the reverse slip. A tech who tries to turn an 18 F rise into Celsius by subtracting 32 gets (18 - 32) / 1.8 = -7.8 C, a negative rise, which is nonsense on its face. Nonsense is the useful outcome: a spec of 50 F was wrong but plausible, and plausible is what nearly got a part ordered.

The second check is the one the supervisor ran: before condemning a heat exchanger on one side's numbers, read the other side. Heat that leaves the boiler water has to arrive in the floor water. If one side is on design and the other is not, look at flows and instruments before the plates.

What changed afterward

The shop's conversion card says it in bold. The laminated card in every truck already carried the temperature formulas. It now leads with one line in bold: A difference converts by 1.8 only. Never add or subtract 32 from a rise, drop, split or delta-T. Below it, the kelvin note: K in a manual means a difference.

Differences carry the word on the ticket. Techs write "18 F rise" or "28 F drop", never a bare "18 F", so a reader can tell a reading from a difference without knowing the job. A ticket that says "secondary 18 F" is ambiguous; one that says "secondary rise 18 F, design 10 C = 18 F" cannot be misread.

Condemning a heat exchanger takes both sides. Before any exchanger replacement is quoted, the ticket records entering and leaving temperatures on both sides, the design figures from the manual with their conversion written out, and a note on flow. This was the rule the supervisor applied in his head. Writing it down means the next tech applies it without the phone call.

References

• The equipment manufacturer's installation and commissioning manual for design temperature differences and flows
• See related: Temperature Conversion and the Delta-T Rule
• See related: The Sensible Heat Formulas for Air and Water
• See related: Units Carried Through Every Line of a Calculation