Heat flux sensor

Soil heat flux is a most important parameter in agro-meteorological studies, since it allows one to study the amount of energy stored in the soil as a function of time.

Typically two or three sensors are buried in the ground around a meteorological station at a depth of around 4 cm below the surface. The problems that are encountered in soil are threefold:

First is the fact that the thermal properties of the soil are constantly changing by absorption and subsequent evaporation of water.

Second, the flow of water through the soil also represents a flow of energy, going together with a thermal shock, which often is misinterpreted by conventional sensors.

The third aspect of soil is that by the constant process of wetting and drying and by the animals living on the soil, the quality of the contact between sensor and soil is not known.

The result of all this is the quality of the data in soil heat flux measurement is not under control; the measurement of soil heat flux is considered to be extremely difficult.

In a world ever more concerned with saving energy, studying the thermal properties of buildings has become a growing field of interest. One of the starting points in these studies is the mounting of heat flux sensors on walls in existing buildings or structures built especially for this type of research. Heat flux sensors mounted to building walls or envelope component can monitor the amount of heat energy loss/gain through that component and/or can be used to measure the envelope thermal resistance, R-value, or thermal transmittance, U-value.

The measurement of heat flux in walls is comparable to that in soil in many respects. Two major differences however are the fact that the thermal properties of a wall generally do not change (provided its moisture content does not change) and that it is not always possible to insert the heat flux sensor in the wall, so that it has to be mounted on its inner or outer surface. When the heat flux sensor has to be mounted on the surface of the wall, one has to take care that the added thermal resistance is not too large. Also the spectral properties should be matching those of the wall as closely as possible. If the sensor is exposed to solar radiation, this is especially important. In this case one should consider painting the sensor in the same color as the wall. Also in walls the use of self-calibrating heat flux sensors should be considered.[5][6]

The measurement of the heat exchange of human beings is of importance for medical studies, and when designing clothing, immersion suits and sleeping bags.

A difficulty during this measurement is that the human skin is not particularly suitable for the mounting of heat flux sensors. Also the sensor has to be thin: the skin essentially is a constant temperature heat sink, so added thermal resistance has to be avoided. Another problem is that test persons might be moving. The contact between the test person and the sensor can be lost. For this reason, whenever a high level of quality assurance of the measurement is required, it can be recommended to use a self-calibrating sensor.

Typical heat flux sensor for studies of radiative- as well as convective heat flux. Photo shows model RC01 with a gold-coated and a black coated heat flux sensor on a metal heat sink. The gold sensor only measures convective heat flux, the black sensor measures radiative as well as convective heat flux. A small air temperature sensor is added to estimate local heat transfer coefficients

Heat flux sensors are also used in industrial environments, where temperature and heat flux may be much higher. Examples of these environments are aluminium smelting, solar concentrators, coal fired boilers, blast furnaces, flare systems, fluidized beds, cokers,...

To do a calibration measurement, one needs a voltmeter or datalogger with resolution of ±2μV or better. One should avoid air gaps between layers in the test stack. These can be filled with filling materials, like toothpaste, caulk or putty. If need be, thermally conductive gel can be used to improve contact between layers.[7] A temperature sensor should be placed on or near the sensor, and connected to a readout device.

The calibration is done by applying a controlled heat flux through the sensor. By varying the hot and cold sides of the stack, and measuring the voltages of the heat flux sensor and temperature sensor, the correct sensitivity can be determined with:

${\displaystyle E_{sen}={\frac {V_{sen}}{\phi _{q}}}}$

where ${\displaystyle V_{sen}}$ is the sensor output and ${\displaystyle \phi _{q}}$ is the known heat flux through the sensor.

If the sensor is mounted onto a surface and is exposed to convection and radiation during the expected applications, the same conditions should be taken into account during calibration.

Doing measurements at different temperatures allows for determining sensitivity as a function of the temperature.

FHF02SC, a thin self-calibrating heat flux sensor. Sensors that are embedded in construction can sometimes be very troublesome to remove if need to be re-calibrated (in a lab). Some sensors incorporate heaters in order to be able to leave the sensor in place while performing a re-calibration.

While heat flux sensors are typically supplied with a sensitivity by the manufacturer, there are times and situations that call for a re-calibration of the sensor. Especially in building walls or envelopes the heat flux sensors can not be removed after the initial installation or may be very difficult to reach. In order to calibrate the sensor, some come with an integrated heater with specified characteristics. By applying a known voltage on and current through the heater, a controlled heat flux is provided which can be used to calculate the new sensitivity.

The assumption that conditions are quasi-static should be related to the response time of the detector.

Heat flux sensor as radiation detector.

The case that the heat flux sensor is used as a radiation detector (see figure to the left) will serve to illustrate the effect of changing fluxes. Assuming that the cold joints of the sensor are at a constant temperature, and an energy flows from ${\displaystyle t>0}$, the sensor response is: ${\displaystyle V_{\mathrm {sen} }=E_{\mathrm {sen} }\left(1-e^{-{\frac {t}{\tau _{\mathrm {sen} }}}}\right)}$

This shows that one should expect a false reading during a period that equals several response times, ${\displaystyle \tau _{\mathrm {sen} }}$. Generally heat flux sensors are quite slow, and will need several minutes to reach 95% response. This is the reason why one prefers to work with values that are integrated over a long period; during this period the sensor signal will go up and down. The assumption is that errors due to long response times will cancel. The upgoing signal will give an error, the downgoing signal will produce an equally large error with a different sign. This will be valid only if periods with stable heat flow prevail.

In order to avoid errors caused by long response times, one should use sensors with low value of ${\displaystyle R_{\mathrm {sen} }C_{\mathrm {sen} }}$, since this product determines the response time. In other words: sensors with low mass or small thickness.

The sensor response time equation above holds as long as the cold joints are at a constant temperature. An unexpected result shows when the temperature of the sensor changes.

Assuming that the sensor temperature starts changing at the cold joints, at a rate of ${\displaystyle {\frac {\mathrm {d} T}{\mathrm {d} t}}}$, starting at ${\displaystyle t=0}$, ${\displaystyle \tau _{\mathrm {sen} }}$ is the sensor response time, the reaction to this is: