Experiments on the propagation of heat #2
Introduction
Hi, I'm Carlo Russo. In this second blog, we're going to do a simple heat transfer experiment using thermistors as sensors.
The experiments in this blog will be based on Fourier's theory of heat conduction which is now nearly two centuries old, but still remains a fascinating subject of physics.
In practice we will repeat a classic physics experiment, the Despretz experiment suppose we have a long metal bar and that it is heated at one end.
The heat generated by the heat source will propagate on the bar and lead to a gradual rise in temperature. Five thermometers along the metal bar, measure the temperature and so we can see how the heat propagates in the bar by reading the temperature values along the bar. This is one of those classic experiments that physics teachers show their students when they talk about thermology in the laboratories. Here is an old Despretz system that we can find nowadays in physics labs.
We want to create a Despretz system using thermistors as thermometers and using a datalogger to read the measures, write them on a file and represent graphically the data obtained.
We will use five identical thermistors (213860-1637 NTC Ring Thermistor) which will be well thermally connected to the bar by means of support screws.
Each thermistor, together with a resistor of suitable value , will constitute a voltage divider. The voltage in the central terminal will be measured by a Pico Data Logger.
The Data Logger
The Pico Datalogger ADC-20 from Pico Technology, is high-resolution and high-accuracy voltage input data logger. It's an acquisition system, capable of reading up to 16 analogue and 4 digital input signals.
We will only use 5 analog inputs for our application.
The voltage that will feed the resistive dividers will be 2.5V. Here is the schematics from Pico Data Logger ADC-20 manual.
We will use the Pico ADC-20 onboard 2.5V rail as a voltage reference, but it would be better to use an external power reference if we want greater accuracy and if we want to use more thermistors, for example to analyze the heat transmission in two directions or with one higher granularity using more thermistors .
NTC's have a non linear resistive response to temperature and there two methods that can be used to calculate temperture:
- Use a lookup table in the form of a scaling file in Picolog;
- Or use equations with using the 'calculate parameters'.
From a didactic point of view they are two very different but both very interesting methods.
The first assumes to carry out measurements with a sample instrument and to create a correspondence table between the voltage value read and the temperature. This method could be the occasion to talk about the problem of choosing the number of sample measurements necessary to have an optimal approximation of the temperature.
The second method, on the other hand, falls within the classic problems of parametric identification and is also very important from a didactic point of view.
I intend to publish both methods applied to the system I have created shortly. In this blog I will limit myself to measuring the voltage on the voltage divider and see how it varies in the five measurement points I have chosen when a heat source starts to supply energy and when the supply stops.
Example of using equations with the use of picologs 'calculate parameters'
Hardware setup as seen in picture.
Using the ADC-24, with 10K thermistors wired in series with 6.8 kOhm resistors, connected to the 2.5v reference.
Here's the method and equations, which uses the Steinhart-Hart equation with modifications to reduce the dynamic range of values required.
Doing the linearisation for each thermistor uses three calculated parameters.
1. Compute natural log of thermistor resistance as first calculated parameter
LnR1 = ln ( Rseries * ( A / ( 2500 - A ) ) )
where A is the voltage across the thermistor, expressed in millivolts and Rseries is the series resistor in this case 6.8K Ohms.
2. Compute the inverse temperature times 10,000 as the second calculated parameter
InvT1 = ( ( ( ( ( 8.863 * A * A ) / 100 ) + 233.9 ) / 100 ) * A ) + 11.303
where A is the natural log of the thermistor resistance (A = LnR1)
3. Compute the temperature as the third calculated parameter
Temp1 = ( 10000 / A ) - 273.15
where A is the inverse temperature times 10,000 (A = InvT1).
The experiment
The system I built to recreate Despretz experiment consists of an aluminum bar with a length of 30 cm and a width of 4 cm.
At one end of this bar I thermally connected eight 11W power resistors to deliver a good amount of heat to the bar.
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The heat generated by them by the Joule effect will propagate by conduction towards the unheated end and will cause the temperature along the bar to rise accordingly.
The heat generated by the resistances will gradually be dissipated by the aluminum bar, mainly due to the effect of convection, and a situation of thermal regime will occur in which, by continuing to power the resistances, the temperature on the bar will remain constant, maintaining a decreasing amplitude profile. going from the heated to the cold side.
If the resistors are no longer powered, there will no longer be a source of heat and the temperature in the bar will begin to decrease in every point until it returns, after a few minutes the same in every point of the bar.
Conclusions and future developments
This project was an opportunity to use thermistors. I have often used them to make thermostats with Arduino but, on this occasion, I wanted to carry out a simple physics experiment.
There are many things to explore, for example using the two methods described above to find temperatures directly, using raw data in a spreadsheet or in software like Matlab for calculating temperatures and especially for viewing in graph format.
It could then be shown how by adding a fin to the aluminum bar, and / or a fan, the dispersion of heat is better and therefore it is possible to dissipate the heat more easily and to maintain a lower temperature.