Measuring small differences in flowing water temperature

I am a retired technology teacher who is interested in building small Stirling engines. I want to be able to measure the heat flow through the displacer chamber of a test bed engine that I am building. The displacer chamber has an electrically heated hot end so measuring the heat input should just be a case of knowing the current and voltage supplying the heaters and multiplying them together .(actually not quite that simple as I plan to use PWM to control the heaters with a PID controller, but that’s another story.) The cold end of the chamber is cooled by water flowing through a series of passageways bored in the aluminium block. A long time ago when I was studying A level physics I remember measuring the thermal conductivity of copper using Searle’s bar apparatus and this is the sort of idea I want to use. I plan to measure the temperature of the water flowing in and out of the cooler and the rate of flow in kg per second. Knowing these and the specific heat capacity of water I should be able to calculate the amount of heat entering the cooler.

So, the problem is that I need to measure the temperature difference between the water flowing in the inlet and out the outlet. I don’t anticipate this difference will be very large, perhaps a few degrees Celsius at most so I will need some precision in these measurements. I am not interested in recording transient changes as the measurements will be made once the system has reached a ‘steady state’ so response time is not likely to be an issue. I think integrating a number of measurements taken over a period of time might help achieve the necessary precision.
What sensors would be suitable for this job. Would it be best to test a number of sensors and select a matched pair? The system will use ordinary water at atmospheric pressure so the temperature range must fall in the range 0 to 100 ⁰C.


― ? ―

As the anticipated temperature difference will be small it would be necessary to know the two temperatures precisely to be able to work out the energy flow through the engine. Absolute accuracy measured to some standard point is less important than being able to know the difference in temperature. My concern is that a sensor that gives readings that are plus/minus 0.5 of a degree Celsius could give a false indication of the energy flow. When a manufacturer quotes figures like plus/minus 0.5 of a degree Celsius is that saying that the sensor will output a value that is within half a degree of the true value but crucially that error is not consistent that say the true value was 40 degree Celsius than sometimes it would output 39.6 and other times 40.5 and that error would vary from instant to instant (probably following a normal distribution) or is the error consistent fore any particular example of the device always reading say 40.2 degrees?

It looks like to are looking for a sensor with 0.1 or 0.01 DegC precision, this will require a temperature sensor that gives consistent readings,
Any in-accuracy you will probably have to calibrate out, rather than rely on a manufacturers spec sheet.

You will need some form of calibration system for temperature, or pay big bucks for laboratory standard equipment.
Even a flow sensor may need to be lab standard.

Tom.... :grinning: :+1: :coffee: :australia:

I think my question is about the nature of the errors likely to be encountered with temperature sensors. Is the often quoted figure of ±0.5 ⁰C saying that the output will vary from instant to instant ±0.5 ⁰C deviation from the true value or is it saying that the output may be within ±0.5 ⁰C but from any instant to the next the error will be constant or at least predictable, like an offset that can be easily corrected?

Regarding the flow sensor I was simply going to weigh the water collected at the output over a period of time. To ensure a steady flow I was going to use a constant head system that recycles water from a bulk tank into a header tank with an overflow that returns to the bulk tank. This should ensure a constant flow rate.

Usually the errors that you find in datasheet is referred to accuracy and not precision.

It mean that there is not +-0.5 degrees variation from one measure to the next one in small amount of time. It mean also that one sensor can differ from another by +-0.5 degrees. You can measure such difference.
If you have some temperature references you can calibrate to achieve more accuracy.
Or you can buy calibrated sensors, for example some Pt100 A class (or better).

Hi Zoomx

That is my understanding of precision too, I have tried to use the term in that way to distinguish it from accuracy. In this case an error in accuracy (ie an offset) is not too critical as I am trying to measure a (small) temperature difference. Do you think taking a number of values over a period of time and averaging them would improve my precision? Also would checking individual sensors against one another allow me so select a pair with matching responses?

If you put yur sensors on the same water with small variation of temperature (eg in a stirofoam box) you can compare the values and estimate the difference between them.
So if you work on temperature difference you can reach a good accuracy because, reading datasheeet, usually the accuracy is
the same over a range of themperature but usually it became worse starting from 40, 50 or 80 °C depending on sensors.
Pt100 are the best for this measurement, you can find a board that can be used with them that you can connect to Arduino. But precise Pt100 are not cheap.
You can use digital sensors like the SiliconLabs Si7051 that has ±0.25 °C: –40 °C to +125 °C
In the range of human body temperature has an accuracy of +-0.1°C
You can find it in small boards ready for Arduino but you have to waterproof it.

1 Like

So I am coming around to the idea of using a pt100 platinum resistance thermometer that is available in a waterproof housing with a MAX31865 amplifier board.

Many thanks

That sounds like the correct solution. They are not super expensive and have a large span so you will be somewhere in the middle of that so it should be stable and repeatable.

PRT100’s are very nice , but often when you include amplifier errors , the result can be not as good as you hope .

I would use ds18b20 sensors , but calibrate them against each other and use in hi resolution settings .
I’ve done this will a drilled aluminium block that you can fit the two sensors in . Using a third thermometer ( which obviously doesn’t need to be particularly special , as the error change verses temperature will be small ) you can get the difference between the two DS probs at various temperatures around the region of interest .
These sensors are usually very close to each other , but have a characteristic curve to the temperature response , giving rise to the +- 0.5c quoted figure .

Data sheet

I remember those Serls bars experiments , lots of possibilities to get wet !!

I am looking at a Sterling engine I made years ago.
I think you will also need to correlate the RPM with the heat transfer.


I bought one, they run really well on coffee..

Tom... :grinning: :+1: :coffee: :australia:


Hi Paul

The performance of small Stirling engines is fascinating. It is very easy to be taken in by a small engine screaming away at several thousand RPM and think that it is very powerful, yet a heavy plodder at a couple of hundred RPM may have a far greater torque and so is a more powerful engine. To make a fast engine slack fits are the order of the day but these allow some pressure to bypass the piston and reduce efficiency. My project will involve measuring the speed and torque generated by the engine as well as the energy input to the engine. I am also interested in answering the question "Does the engine produce power on the return stroke?" It is hard to believe but we just don't know what goes on in these little engines.

I'm an analog guy so my first thoughts revolved around thermocouples, PRT's or LM335's. However the issue then is taking a very small voltage difference and generating an accurate and stable reading.

The DS18B20 at first sight looks an attractive proposition, with a resolution of 0.06 deg C, and I'm sure the errors and drift can be balanced out. However if the temp difference you expect is small (say 6 degrees) then you are only seeing 1% resolution.

An analog solution then potentially offers better results;
thermocouples can be ruled out as cu/constantan eg gives only 0.04mV/deg c.
so I'd consider PTR's - good sensitivity, very stable, not expensive; used in a bridge configuration to give a temperature difference, and measured with an instrumentation amplifier & ADC will give very precise results.


Hi John

Your idea of putting the two platinum resistance sensors into a bridge circuit is very interesting and I will look at it in more detail. The temperature difference expected will be small but possibly it could be increased by reducing the water flow rate to get something that will be easier to measure.


That is an interesting question, the power stroke pushing the piston out is due to the internal pressure being greater than atmospheric.
When the cycle cools, is their a reverse difference in pressure differential to push the piston back down, or does the flywheel effect complete the stroke because the internal pressure returns to "near atmospheric" so no differential pressure.

Great experiment...
Tom... :grinning: :+1: :coffee: :australia:

Hi Tom

Consider a sealed cylinder of gas. At room temperature the pressure is 1 atmosphere. Warm the gas and it expands raising the pressure. This is good because you can use the pressure to drive the piston along the power cylinder doing some work. If the gas is then cooled to room temperature the pressure in the cylinder will return to 1 atmosphere. Now if the external air pressure is 1 atmosphere also then there will be no force applied to the back of the piston to push it back along its cylinder. In real Stirling engines there is a flywheel that helps return the piston, but the engines can run without the flywheel. Now maybe the momentum of other moving parts in a "flywheelless" engine is sufficient to return the power piston but other evidence suggests that there is a negative pressure (Even in engines that are ambient air cooled) inside the engine at the start of the return stroke. If this is the case then some useful work could be done during the return stroke.

This negative pressure probably results from some air leaking past the piston/displacer gland during the power stroke.

There seems to be a gap between the classical theory of how Stirling engines operate and empirical observations and that is interesting and worthy of investigation.

I have that one too!

DS18B20 are good sensor, you can have many of them on only 3 wires and each one has serial number, so you can calibrate all sensors without confusion.

Analog sensors have problem with noise, power noise usually but also ambient noise. But if you have to measure small difference then they are better maybe the best solution if well calibrated.
They are the only solution when you are close to 100°C or more since only few digital sensors works well at these temperatures.