Heat Flux Sensor - Properties

Properties

A heat flux sensor should measure the local heat flux density in one direction. The result is expressed in watts per square meter. The calculation is done according to:

Where is the sensor output and is the calibration constant, specific for the sensor.

As shown before in the figure to the left, heat flux sensors generally have the shape of a flat plate and a sensitivity in the direction perpendicular to the sensor surface.

Usually a number of thermocouples connected in series called thermopiles are used. General advantages of thermopiles are their stability, low ohmic value (which implies little pickup of electromagnetic disturbances), good signal-noise ratio and the fact that zero input gives zero output. Disadvantageous is the low sensitivity.

For better understanding of heat flux sensor behaviour, it can be modeled as a simple electrical circuit consisting of a resistance, and a capacitor, . In this way it can be seen that one can attribute a thermal resistance, a thermal capacity and also a response time to the sensor.

Usually, the thermal resistance and the thermal capacity of the entire heat flux sensor are equal to those of the filling material. Stretching the analogy with the electric circuit further, one arrives at the following expression for the response time:

In which is the sensor thickness, the density, the specific heat capacity and the thermal conductivity. From this formula one can conclude that material properties of the filling material and dimensions are determining the response time. As a rule of thumb, the response time is proportional to the thickness to the power of two.

Other parameters that are determining sensor properties are the electrical characteristics of the thermocouple. The temperature dependence of the thermocouple causes the temperature dependence and the non-linearity of the heat flux sensor. The non linearity at a certain temperature is in fact the derivative of the temperature dependence at that temperature.

However, a well designed sensor may have a lower temperature dependence and better linearity than expected. There are two ways of achieving this:

As a first possibility, the thermal dependence of conductivity of the filling material and of the thermocouple material can be used to counterbalance the temperature dependence of the voltage that is generated by the thermopile.

Another possibility to minimise the temperature dependence of a heat flux sensor, is to use a resistance network with an incorporated thermistor. The temperature dependence of the thermistor will balance the temperature dependence of the thermopile.

Another factor that determines heat flux sensor behaviour, is the construction of the sensor. In particular some designs have a strongly nonuniform sensitivity. Others even exhibit a sensitivity to lateral fluxes. The sensor schematically given in the above figure would for example also be sensitive to heat flows from left to right. This type of behaviour will not cause problems as long as fluxes are uniform and in one direction only.

To promote uniformity of sensitivity, a so-called sandwich construction as shown in the figure to the left can be used. The purpose of the plates, which have a high conductivity, is to promote the transport of heat across the whole sensitive surface.

It is difficult to quantify non-uniformity and sensitivity to lateral fluxes. Some sensors are equipped with an extra electrical lead, splitting the sensor into two parts. If during application, there is non-uniform behaviour of the sensor or the flux, this will result in different outputs of the two parts.

Summarising: The intrinsic specifications that can be attributed to heat flux sensors are thermal conductivity, total thermal resistance, heat capacity, response time, non linearity, stability, temperature dependence of sensitivity, uniformity of sensitivity and sensitivity to lateral fluxes. For the latter two specifications, a good method for quantification is not known.