## Tuesday, November 01, 2011

### Hot plate PI controller - Part 5: Boiling water and measuring with thermistor

I made a new mistake in my attempt to make a hot plate PI controller: The thermistor I selected from eBay was an unbranded China thermistor marked with "10k ohm 103 NTC Thermistor"with no datasheet. I thought it would be easy to obtain the datas for the thermistor, but so far I have not been able to find any other info than what the seller is saying:

Model: CP_RM_103 NTC Thermistor
Resistance: 10KΩ
Resistance tolerance: +/- 10%
Temperature: 30°C to +125°C

I have sent an email to the seller as a last effort to get a datasheet for the thermistor, but I have doubts that I will get it.

I wanted to set up a test to check the accuracy of the thermistor in combination with the pre set parameters in the arduino library for thermistors. I soldered a wire to the thermistor, filled a pot with 1 liter of spring water, submerged the thermistor and boiled the water. When boiling temperature 100°C is reached the chart for temperature with stabilize at 100 degrees as water is vaporized.

First some theory:
Thermodynamics has equations describing how a volume will be heated. When there is no flow in or out of the volume the heating equation reduce to:

Cp*ρ*V*dT/dt=P+h(T0-T)

Where
Cp is specific heat capacity. For water Cp=4181.3 J/(kg*K)
ρ is the density. For water ρ=1000 kg/m^3
V is the volume. For my experiment I use 1 liter=1e-3 m^3
T is the temperature in the volume.
T0 is the temperature of the neighboring. The air temperature is about 22°C
P is the power of the heating source. I use two different boiling plates with 1.4 and 1.5 kW
h is the heat conduction number

If no energy is transferred to the environment with no other losses whatsoever I get:
Δt=Cp*ρ*V*ΔT/P

I am using two different hot plates:
1. A 1.5 kW standard hot plate. Ideal time for boiling 1l water should be 262 seconds, about 4 minutes.
2. A 1.4 kW induction hot plate. Ideal time for boiling 1l water should be 281 seconds, about 4,5 minutes.

The ideal heating time is based on the tap water being 6°C.

After modifying the LabVIEW VIs used with the thermistor and servo to also save raw voltage data to disk and importing to excel I get these curves: A couple of things can be observed from the charts:
1. The heating curve for the induction hot plate is very erratic. This is likely because induction is basically fast alternating current through a coil. This creates a magnetic field that again induces current in the sensor wire. If better results are to be obtained with an induction cooker I need a shielded thermistor.
2. Both measured heating curves for the induction and standard hot plate has a measured boiling temperature of about 110°C. This is probably due to wrong values for this sensor set for the Steinhart-Hart equation.
3. The zero crossing with the y-axis is above the temperature of the tap water temperature. This is again probably due to wrong values in the Steinhart-Hart equation.
4. Some drops are observed for the standard hot plate. This is due to different temperatures when the thermistor touched the pot and when it was only in contact with water.
5. The slope for the induction cooker is very close to the ideal curve, thus the induction cooker is very efficient at transfering energy into cooking water.
6. The induction hot plate and pot can be modeled as an integrator without time delay. The standard hot plate can probably be modeled as an integrator with a time delay included. When heating a larger amount of water I am expecting more energy to be transfered to the environment, and  the curves will probably take the shape of a "time-constant with time-delay" process.
Now I need to search a little more to try finding some information about the sensor specs. This in combination with the measured curves will probably give me everything I need to know to calibrate the thermistor.