Heat Flux & Heat Transfer Science

Heat Flux Measurement

This chapter contains an  overview of "the art of heat flux measurement". In the same 'Heat Flux & Heat transfer science section: 

• Measurement of the heat transfer mechanism, in particular the heat transfer coefficient.

• Free copy of the more detailed Scientific Literature.

For application of heat flux sensors in specific applications, like meteorology, or building physics, see Fields of application.

What everybody should know

Heat flux is the rate of energy transfer through a given surface. This quantity can be measured using a heat flux sensor. The measurement of heat flux is of importance to many sciences. Most common applications are in building physics, where the heat flow through walls is one of the factors determining the indoor climate,  in agricultural meteorology, where the heat flux into the soil is a parameter in the study of evaporation of water, and biology to measure heat flux from humans or animals. The accurate measurement of heat flux can lead to energy saving in buildings and to more efficient use of water in irrigated agricultural area's. 

A certain heat flux is created by a non equilibrium in temperature. The necessary energy is transferred either by radiation, conduction or flow.

With a heat flux sensor it is possible to measure conductive heat transfer. An additional possibility, when using techniques with heaters, to study the transfer coefficients (typically from the air to the sensor).

Hukseflux can offer state-of-the art high-accuracy technology, like its newly developed self-calibrating technology of HFP01SC. For many applications however the conventional HFP01 might be sufficient. In some cases the sensor resistance plays a role (resistance error 1) or the response time, and UT03 can better be used. With the DT01 thermopile, you can construct your own heat flux sensor. The theory in this section will offer a clue what error sources can be expected.

Heat flux sensors are usually surrounded by the substance of the object that is studied. This substance we call the medium.  Sometimes sensors are mounted on the object.

Generally, a heat flux sensor will consist of a plate with a differential temperature sensor between the top and bottom. Assuming that the thermal conductivity of the plate is constant and the flow is static, the heat flux is proportional to the measured temperature difference. A schematic view is below.

A schematic view of a heat flux sensor. The majority of heat flux sensors is based on a thermopile. A single thermocouple will generate an output voltage that is proportional to the temperature difference between the hot- (5) and cold (4) side. This temperature difference is proportional to the local heat flux (6). Using more thermocouples (1) and (2) in series, will enhance the output signal. The thermopile is embedded in a filling material, (3), usually a plastic. Each individual sensor has its own sensitivity, E_sen, usually expressed in Volts output, V_sen, per Watt per square meter heat flux. The flux H is calculated H = V_sen/ E_sen.

What everybody should know, but rarely is aware of

The key point to doing a good measurement is to understand how, when introducing a heat flux sensor in the medium or on the object, the sensor will disturb the thermal flow. Two common error sources can be seen in the pictures below.

A common error source, the resistance error. Increased or reduced local resistance will cause a change in total thermal resistance of the object that less or more heat (1) will flow through the part of the material (3) where the sensor (2) is mounted. lines such as (3) represent isotherms.

The deflection error. Non-matching thermal conductivity's of sensor (2) and medium (around the sensor) and the fact that the sensor is in-homogeneous cause that the sensor experiences a non-representative flow (1).

Recent experimental research (1997) has shown convincingly that the major error source in many applications is the deflection error and also that the accuracy of existing measurements is very low.

Heat flow measurement error sources, theory

Several authors have analyzed possible error sources in the heat flux measurement. The conclusions are summarized in the table below. There are other error sources, like non-linearity, that are not mentioned. Based on general experience with thermal sensors, the contribution of these is considered to be small compared to the effects that are mentioned.

Possible error sources in a heat flux measurement.

The resistance error 1 can often be estimated on theoretical grounds, knowing the approximate dimensions and thermal conductivity's that are involved. The resistance error 2 is an important error source, which simply must be avoided by creating a good thermal contact between medium and sensor. Depending on the circumstances one can estimate the temperature error on theoretical grounds.

Heat flux measurement error sources, experimental research

Surprisingly, experimental research to check the above theory on error sources has only been done in 1997. This experiment has shown that even the carefully designed sensors show behavior that cannot be explained using the theory for homogeneous sensors. Over a thermal conductivity range from 0.1 to 1.7 W/m.K, a typical range for soils and building materials, the range of errors was about 30%. This is much less accurate than theory had ever predicted.

The explanation for the large errors is in deflection error 2. This error accounts for the fact that a typical heat flux sensor will have a high thermal conductivity in the center, where the actual sensor is located, and a lower conductivity outside the center.

The graph below shows the results of the experiment, making a comparison with the theoretically predicted behavior by Philip.

The deviation in % of the sensitivity (axis marked 1) of a typical heat flux sensor, as a function of the thermal conductivity of the medium(axis marked 4). As a reference sensitivity, the manufacturers data are used (2).  Also shown: the improvement that can be attained using a self-calibrating heat flux sensor (3). (see below)

Heat flux measurement: state of the art, the self calibrating heat flux sensor

A summary of the conclusions from previous theoretical and experimental research (all performed in the laboratory) is that, when the sensor is applied in a optimal way, the deflection error, temperature error and errors in the calibration factor are the largest error sources.

Going from the laboratory to a field environment, there are additional problems; The first is that one cannot judge the condition of the sensor, its wiring and the data processing. In other words, it is difficult assess the stability of the measurement. Especially in meteorological applications, in hostile outdoor environments, this is judged to be the largest error source. This is why, although some sensors seem to have an accuracy in the laboratory that is sufficient, in the outdoor environment their use still cannot be recommended. The second issue is the temperature error. In the majority of applications the sensor will measure in a range of temperatures. Relatively mild conditions; a 20 degree range and 0.2%/K temperature dependence will already produce a 4% error. The state of the art is defined by the Hukseflux patent pending self-calibrating technique; For the major error sources, an improvement can be obtained by using the self calibration technique.

Also in biological/medical applications, where the sensor is usually mounted on the skin, the self calibrating principle offers an extra means of quality assurance of proper connection.

This completely new sensor design has been tested in static situations in various environments.

The result of this study confirms theory. While ordinary data will show deviations over a 25% range, for conductivity's from 0.2 to 1.7, the corrected values (using the self calibrating technique) show deviations over a 10% range only. This can be considered to be an enormous improvement.

The figure above also shows the deviation of the sensitivity of the self calibrating heat flux sensor with and without using the self calibration, as a function of the thermal conductivity of the medium. As a reference sensitivity, the manufacturers data are used. The conclusion of this experiment is that the self calibration technique works, and that it offers the highest accuracy and quality assurance of the measured data that is currently available.

Additionally the measurement contains information on the thermal properties of the medium. In meteorological experiment it is common practice to have some redundant measurements for reasons of quality control. The added graph shows a clear dependence of the signal amplitude on the soil moisture content.

The pulse response of the self calibrating heat flux sensor in one medium with variable moisture content. These graph shows that the pulse response also contains information on the moisture content (Lambda stands for thermal conductivity, Lambda=0,17; dry soil, Lambda=1,7; saturated soil), a property that can be used in meteorological applications.

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