Field of the invention

The invention relates to a sensor for measuring a heat flux comprising a body that acts as a heat sink, well conducting and absorbing heat, with a thermal conductivity larger than 10 W/(m K) and a heat capacity larger than 18 J / K with on a measurement side an absorptive heat flux sensor operable to absorb thermal radiation and a reflective heat flux sensor operable to reflect thermal radiation, both sensors being substantially equally sensitive to convective heat flux.

The invention also relates to a system comprising such a sensor and a method of estimating a convective heat flux and a heat transfer coefficient and/or an ambient air temperature using such a sensor.

Background

A sensor for the measurement of heat transfer using a combination of absorbing and reflecting temperature sensors for use in an oven is known from EP 3568639. A measuring instrument is connected to the sensor for monitoring the local heat fluxes, calculated from temperature changes of the sensors in the oven, on the basis of the absorptive and the reflective sensor signals.

Use of temperature controlled absorbing and reflecting temperature sensors is described in ISO 7726 Clause C 2.1 which describes measurement of plane radiant temperature by a heated sensor consisting of a reflecting disk and an absorbing disk, each containing a temperature sensor.

Convective and radiative heat flux may also be separated by performing a separate radiative and absorptive (total), radiative plus convective, heat flux measurement, for example using a radiative heat flux sensor equipped with an optical filter, protecting it from convection. However, using such sensors it is difficult to match directional properties (field of view, expressed as solid angle in steradians or sr) of the 2 heat flux sensors, and as a result the sensors do not have the same sensitivity to convective heat flux, so that convective and radiative flux cannot accurately be separated. Also it is no longer possible to apply the same calibration procedure, using conductive heat flux originating from a calibration heater, to the two heat flux sensors.

When using an absorptive and a reflective heat flux sensor, the convective heat flux may be caused by a difference in air temperature relative to the sensor body, and also depends on the heat transfer coefficient, which is a function of the air velocity of the ambient air. To distinguish between these two effects, a measurement of the temperature of ambient air is required, which cannot be easily and accurately carried out.

It is therefore an object of the invention to provide a thermal sensor and a measurement system of a compact and fail-safe construction with which a radiative and convective heat flux from the local environment to the sensor can be accurately measured. It is a second object of the invention to facilitate calibration. It is another object of the invention to provide such a sensor and measurement system which can be operated and also give an estimate of the heat transfer coefficient without a measurement of the ambient air temperature.

Summary of the invention

Hereto a sensor according to the invention is provided with a heating member in heat conducing contact with the body for heating the body to a predetermined temperature, an absorptive heat flux sensor operable to absorb thermal radiation and a reflective heat flux sensor operable to reflect thermal radiation on a measurement side of the body and a temperature sensor that is thermally coupled with the body for measuring the body temperature, wherein the heat flux sensors have a substantially similar field of view between 1 .5 p and 3 p sr.

By the use of the absorptive and reflective heat flux sensors having overlapping, preferably substantially identical, fields of view, separate convective and radiative heat fluxes can be accurately determined at different temperatures of the heat flux sensors and the body carrying the heat fluxsensors, by control of the heating member. This results, by calculation, in an estimate of the ambient air temperature without the need of an additional ambient air temperature sensor and at the same time results in an accurate calculation of the convective heat transfer coefficient of the ambient air to the sensor.

By the heating member, the sensor according to the invention can be controlled to an exact temperature or power consumption that is relevant to the situation that is investigated. The sensor according to the invention can be used for instance for studies to cooling efficiency of servers in data centers in which the sensor body will represent a typical electronics or processor board and can be operated at a predetermined representative power or can be controlled to a predetermined representative temperature.

The measurement values of the sensor according to the invention can be verified for quality assurance by measuring at more than 2 body temperature levels, looking if the model of heat transfer fits the measurements. Further quality assurance of the measurements made with the sensor according to the invention is possible by comparing the total power in W required to keep the sensor at a stable temperature to the measured heat fluxes in W/m ² and the sensor body surface area in m ² .

It is noted that US 5,216,625 discloses a temperature sensor with a heated body of anodized aluminium, nickel plated copper. The metal body forms a thermal sink and comprises sensors that are covered with a thin thermally reflective coating such as gold of aluminium, reflecting any extraneous radiation heat flow without affecting the convective-conductive heat flow component. A part of the body is heated via an electric resistance heater. No separate convective and conductive heat fluxes can be measured with the known sensor.

In an embodiment of a sensor according to the invention, the field of view of the absorptive and reflective heat flux sensor is substantially 2 p sr and the sensors are substantially mounted in the same plane, if flat parallel within 10 °, and no more than 0.05 m separation between the plane of mounting of one sensor and centre point in the plane of mounting of the other sensor, if curved with a curvature radius between 0.01 and 1 m, and no more than 0.05 m separation between the axis of one sensor and centre point on the axis of the other sensor.

This way, the sensors are exposed to substantially the same convective and radiative heat fluxes.

The surface area of the heat flux sensors according to the invention may be between 10 ^-6 and 10 ^_2 m ² , the reflectivity of the reflective heat flux sensor is between and 0.5 and 1 , the absorptivity of the absorptive heat flux sensor is between 0.8 and 1 ; typical materials are gold with a reflectivity of 0.9 or nickel with a reflectivity of 0.8, and black high temperature paints with an absorption of 0.9.

In an embodiment of a sensor according to the invention, the heat flux sensors are each provided with a respective calibration heating element.

The calibration heating elements according to the invention offer the advantage that the reflective (convective) heat flux sensor and the absorptive (radiative plus convective) heat flux sensor can be calibrated in exactly the same way using a simple procedure, i.e. applying a known power to these elements, calculating the heat flux and comparison to the sensor output signals. For the calibration, the sensors do not need to be transported to a specialized test facility, and can be put at the measurement site at regular intervals.

A system according to the invention comprises a control unit connected to the heat flux sensors, the heating member and the temperature sensor, the control unit being adapted for: imparting at least two different temperatures to the body, receiving for each temperature a heat flux value from the absorptive sensor and from the reflective sensor, and determining from the heat flux and body temperature values, a conductive and a radiative heat flux, an air temperature, a convective heat transfer coefficient Ctr and/or an air velocity near the sensor.

On the same side of the body the absorptive heat flux sensor, which measures radiative and convective heat flux, as well as the reflective heat flux sensor measuring predominantly convective heat flux are situated. By subtracting the two measured heat fluxes, the radiative flux can be calculated.

Measuring the heat flux with the reflective sensor, at a single known sensor body temperature, if the ambient air temperature is known, the local heat transfer coefficient (which is a function of air velocity) can be calculated.

The heat fluxes in W/m ² , the body temperature in °C , possibly combined with the power in W needed to maintain a fixed body temperature and separately measured or estimated ambient air temperature in °C, are used to calculate all local modes of thermal transport separating radiation and convection.

In an embodiment of a system according to the invention, the control unit is adapted to: store heat flux and temperature values measured by the absorptive heat flux sensor and the reflective heat flux sensor, and the temperature sensors measure convective heat flux signals F convection, i , F convection, 2 generated by the reflective heat flux sensor at two sensor temperatures Tsen, 1 , T _S en, 2, determine the convective heat transfer coefficient Ctr by:

Ctr (F convection, 2 “ F convection, 1 ) / ( Tsen, 1 - Tsen, 2 ) with positive heat flux from surrounding environment to the sensor. and/or calculate an ambient air temperature Tair at or near the sensor by :

Tair ^— Tsen, 1 F convection, 1 ( Tsen, 1 - Tsen, 2 ) / (F convection, 2 “ F convection, 1 )

A velocity of the ambient air, v _ai r , may be determined on the basis of the convective heat transfer coefficient Ctr The control unit may be adapted for calculating the ambient air velocity v _ai r, using an empirical formula valid for the sensor geometry and the direction of the ambient air flow, for example by:

Vair = ((Ctr -B)/A) ² wherein A and B are stored in a look up table or are calculated in the control unit. In an embodiment of a system according to the invention, for each calibration heating element, a surface area A and a resistance R is stored, the control unit being adapted to: calculate a calibration heat fluxcDc for each sensor as a result of a power P supplied to the calibration heating element measuring a sensor output U and determining for each sensor a sensor sensitivity E on the basis of the sensor output U and calibration heat fluxcDc.

In such a system, the control unit may be adapted to determine the sensitivity E by:

E = U/Fo.

Brief description of the drawings

An embodiment of a sensor, a system comprising such a sensor and a method using such sensor will by way of non-limiting example be described in detail with reference to the accompanying drawings. In the drawings:

Figure 1 shows a perspective view of a sensor for measuring a heat flux in accordance with the present invention;

Figure 2 shows a cross-sectional side view of a measurement side of the 2 sensors, absorptive and reflective, for measuring a heat flux in accordance with the present invention;

Figure 3 shows a perspective view of a measurement side of the 2 sensors, absorptive and reflective, for measuring a heat flux of the in accordance with the present invention;

Figure 4A shows a perspective view of a substantially flat mounting plane of the 2 sensors, absorptive and reflective, for measuring a heat flux in accordance with the present invention;

Figure 4B shows a perspective view of a curved mounting plane of the 2 sensors, absorptive and reflective, for measuring a heat flux in accordance with the present invention;

Figure 5 shows a perspective view of a sensor for measuring a heat flux of the invention in accordance with the present invention;

Figure 6 shows a schematic view of a system for measuring a heat flux in accordance with the present invention; Figure 7 shows a flowchart of a method of estimating air temperature and/or convective heat transfer coefficient, and to calibrate all heat fluxsensors in accordance with the present invention.

The sensors, systems and features thereof are shown schematically and not drawn to scale.

Detailed description of the invention

Figure 1 shows a perspective view of a sensor 1 for measuring a heat flux in accordance with an embodiment of the present invention. The sensor comprises a body 2 with a plurality of sides 3, 4, 5, 6, 7, 8, an absorptive heat flux sensor 9 operable to absorb thermal radiation and a reflective heat flux sensor 10 operable to reflect thermal radiation. The sensor may optionally be equipped with an ambient air temperature sensor 13. The body 2 comprises at least one temperature sensor 11 for measuring the temperature of the body and at least one heating member 12.

The absorptive heat flux sensor 9 operable to absorb thermal radiation is further referred to as absorptive sensor. This absorptive sensor 9 measures both convective and thermal radiation. The reflective heat flux sensor 10 operable to reflect thermal radiation is further referred to as reflective sensor. The reflective sensor 10 measures predominantly convective heat flux. The body 2 is well conducting heat, typically made of metal with a thermal conductivity of larger than 10 W/(m K) and a heat capacity larger than 18 J / K typically made of metals such as aluminium, brass or steel. Each side of the body 3, 4, 5, 6, 7, 8 is a predominantly flat surface with a different spatial orientation. One side 3 of the body 2 is equipped with the absorptive sensor 9, the reflective sensor 10 and is further referred to as measurement side 3. The absorptive sensor 9 and the reflective sensor 10 on the measurement side 3 have a substantially similar mounting surface and field of view as further described in figures 3, 4A and 4B, for the respective absorption and reflection of thermal radiation to be comparable and the sensitivity to convection to be comparable. The absorptive and reflective sensors may be placed anywhere on the measurement side 3, as long they have a substantially similar exposure of their surface area to thermal radiation and convection. The absorptive sensor 9 is typically black coated to absorb thermal radiation, the coating may be made of a black high temperature paint qualifying as high absorptivity layer 14. The heat flux sensor may be made using a thermopile sensing element encapsulated in a plastic 16, or another method measuring a temperature difference across a solid layer and presents a thermal absorptivity between 0.8 and 1 . The absorptive sensor 9 measures both a convective and a radiative heat flux, F convection + F radiation, through its surface on the measurement side 3. The reflective sensor 10 is typically gold coated to reflect thermal radiation, may be made of a gold, silver, aluminium or nickel layer qualifying as high reflectivity layer 15 on a heat flux sensing element 17 and presents a thermal reflectivity between 0.5 and 1 . Heat flux sensing elements 16, 17 convert the thermal energy of absorbed or emitted heat flux for each sensor into an output signal, in case of a thermopile an electrical voltage. The reflective sensor

10 measures predominantly a convective flux® convection through its surface on the measurement side 3.

By subtracting the heat flux measured by the reflective sensor 10, F convection, from the heat flux measured by the absorptive sensor 9, F convection + F radiation, through their surfaces of substantially equal sensitivity to convective heat flux on the measurement side 3, the radiative heat flux® radiation may be estimated. The sensor 1 is therefore able to separately measure radiant and convective heat transfer on the measurement side 3. Mathematical corrections may be applied for reflectivity and absorptivity not equal to 1 .

The heating member 12 is positioned in heat conducting contact with the body 2 and may be used to heat the body 2 to a predetermined temperature or at a predetermined power. Due to the body’s high thermal conductivity, typically made of aluminium, brass or steel, combined with its mass, expressed as heat capacity, it internally has a low thermal resistance and the body is uniformly heated to the predetermined temperature, T _S en, via heat conduction from the heating member. The temperature sensor

11 thermally coupled with the body 2 is used to measure the temperature of the body. By controlling the body 2 to a predetermined temperature via the heating member 12 and the temperature sensor 11 , radiative and convective heat transfer to an object of that particular temperature T _S en, relevant to a user, can be simulated and measured. By measuring convective heat transfer using the absorptive sensor 9 and the reflective 10 sensor at multiple temperature levels of the body 2, from F convection, i - F convection, 2 at two or more predetermined temperatures Tsen, 1 , T _S en, 2, the air temperature Tair and heat transfer coefficient Ctr can both be calculated, eliminating the need for a separate air temperature measurement, and improving the level of quality assurance of the heat transfer measurements:

Ctr (F convection, 2 “ F convection, 1 ) / ( Tsen, 1 - Tsen, 2 ) with positive heat flux from surrounding environment to the sensor, and/or calculate an ambient air temperature Tair at or near the sensor by :

Tair ^— Tsen, 1 F convection, 1 ( Tsen, 1 - Tsen, 2 ) / (F convection, 2 “ F convection, 1 )

The optional ambient air temperature sensor 13 can be also used to separately measure an air temperature. An ambient air velocity v _air can further be calculated from the heat transfer coefficient using an empirical formula valid for the sensor geometry and the direction of the ambient air flow, for example by:

Vair = ((Ctr -B)/A) ² where A, B are constants empirically determined or taken from theory.

Figure 2 shows a cross-sectional side view of the measurement plane 3 of the sensor 1 for measuring a heat flux of Figure 1 , according to an embodiment of the invention. In this embodiment, the absorptive sensor 9 comprises, besides the high absorptivity layer 14 and the thermopile sensing element

16, a calibration heating element 18. Furthermore the reflective sensor 10 comprises, besides the high reflectivity layer 15 and the heat flux sensing element 17, a calibration heating element 19.

Each calibration heating element 18, 19 is placed between the high absorptivity layer 14 and the thermopile sensing element 16 or between the high reflectivity layer 15 and the heat flux sensing element

17, respectively. Calibration heating elements 18, 19 may be identical and/or built integrally within the absorptive and reflective sensors 9, 10. The sensitivity, surface area and electrical resistance of the calibration heating elements 18, 19 are predetermined. They allow calculation of a calibration heat flux for a measured voltage over or current through, the calibration heating element.

By incorporating calibration heating elements 18, 19 on the heat flux sensors 9, 10, the sensors can be calibrated using a simple and unique procedure for both sensors, where the ratio of the measured calibration heat flux, F ₀ , to an output signal U of the thermopile or heat flux sensing element 16, 17 can be used to calculate a sensitivity E of the absorptive sensor and the reflective sensor 9, 10 according to:

E = U/Fo

In other embodiments, alternative calibration functions may also be used. Heat fluxes may also be corrected for losses to the environment, edge effects etc. During calibration the heat flux sensor surfaces may be thermally insulated. The emissivity and absorption of the sensor surfaces may be separately estimated by inspection or by experiment.

Figure 3 shows a perspective view of the measurement surface 3 of the sensor 1 for measuring a heat flux of Figure 1 in accordance with an embodiment of the present invention. The predominantly flat measurement surface 3 is equipped with an absorptive sensor 9 and a reflective sensor 10 disposed at any location on the measurement surface and comprising the high absorptivity layer 14 and the high reflectivity layer 15, respectively, exposed to environmental heat fluxes. Each of the absorptive and reflective sensors 9, 10 have a substantially similar field of view 20, 21. Each field of view 20, 21 expands substantially 180 degrees in a longitudinal and in a transverse direction in an entrance plane at the measurement side 3, in other words a solid angle of 2p sr. Furthermore, the high absorptivity layer 14 and the high reflectivity layer 15 are each mounted in a plane further described as a plane of mounting 22, 23.

Figure 4A shows a perspective view of a plane of mounting 22, 23 of the high absorptivity layer 14 and of the high reflectivity layer 15 of the sensor 1 for measuring a heat flux of Figure 1 , which are substantially mounted side by side and in the same plane of mounting, where an angle between the two planes 22, 23 does not exceed 10 ° and a distance h between the plane of mounting of one sensor and a centre of the other sensor in its plane of mounting does not exceed 0.05 m. Sensors may also be curved, in which case the plane of mounting is also curved.

Figure 4B shows a perspective view of a curved plane of mounting 22, 23 of the high absorptivity layer 14 and of the high reflectivity layer 15 of the sensor 1 for measuring a heat flux of Fig. 1 , where a curvature radius of each plane of mounting is between 0.01 and 1 m and the separation h between the axis (A1) of one sensor and centre point on the axis (A2) of the other sensor does not exceed 0.05 m.

Figure 5 shows a perspective view of a sensor 25 for measuring a heat flux in accordance with an embodiment of the present invention. The sensor comprises a body 26 with a plurality of sides 27, 28, 29, 30, 31 , 32, at least two absorptive heat flux sensors 33, 35, 37, 39, 41 , 43 operable to absorb thermal radiation and at least two reflective heat flux sensors 34, 36, 38, 40, 42, 44 operable to reflect thermal radiation. The sensor 25 may optionally be equipped with an ambient air temperature sensor 46. The body 26 comprises at least one body temperature sensor 45 and at least a heating member 47.

The at least two absorptive heat flux sensors 33, 35, 37, 39, 41 , 43 operable to absorb thermal radiation are further referred to as absorptive sensors, and the at least two reflecting heat flux sensors 34, 36, 38, 40, 42, 44 operable to reflect thermal radiation are further referred to as reflective sensors. They function identically and may be placed identically as the absorptive and reflective sensors described in the embodiment of Figure 1 , where each side 27, 28, 29, 30, 31 , 32 is also a flat surface with a different spatial orientation. Further the absorptive sensor and the reflective sensor have also a substantially similar mounting plane and field of view as previously described in Figures 3 and 4. In the present embodiment at least two sides 27, 28, 29, 30, 31 , 32 are each equipped with an absorptive sensor, a reflective sensor and are further referred to as measurement sides, for the respective sensitivities to convective flux and absorption and reflection of thermal radiation to be comparable. The sensors may also be calibrated with respective calibration heating element such as shown previously in Figure 2.

The heating member 47 is positioned in heat conducting contact with the body 26 and may be used to heat the body 26 to a predetermined temperature, T _Se n. Due to the body’s thermal conductivity, typically made of aluminium, brass or steel, and internally low thermal resistance the body is uniformly heated to the predetermined temperature via heat conduction from the heating member. The temperature sensor 45 thermally coupled with the body 26 may be used to measure the temperature of the body. By controlling the body 26 to a predetermined temperature via the heating member 47 and the temperature sensor 45, radiative and convective heat transfer to an object of that particular temperature with surfaces of different orientations 27, 28, 29, 30, 31 , 32, relevant to a user, can be simulated and measured for each orientation.

By measuring convective heat transfer using the absorptive sensors 33, 35, 37, 39, 41 , 43 and the reflective sensors 34, 36, 38, 40, 42, 44 at multiple temperature levels of the body 26, from the convective heat values F convection, 1 , F convection, 2 at two or more predetermined temperatures T _Se n, i, T _Se n,2, the air temperature Tair and heat transfer coefficient Ctr can both be calculated in the vicinity of each the at least two measurement sides, eliminating the need for a separate air temperature measurement, and improving the level of quality assurance of the heat transfer measurements, identically as in the embodiment of Figure 1 . Furthermore the ambient air velocity Vairnear each of the at least two measurement sides, can also be determined as in the embodiment of Figure 1 .

Figure 6 shows a schematics of a system 50 for measuring a heat flux comprising a sensor 1 , 25 of Figure 1 or Figure 5 for measuring heat flux according to an embodiment of the invention. The system 50 further comprises a control unit 60 in electrical connection with at least one of: the absorptive and/or a reflective sensors 9, 10, 33, 34, the temperature sensor 11 , 45 and the heating member 12, 47 and a terminal 61 .

The system may include an ambient air temperature measurement 13, 46. The control unit may also be described as a measurement and control unit. The system, sensor plus measurement and control unit, can be used in studies of heat transfer, for example in studies to cooling efficiency of servers in data centres. The body 2, 26 will represent a typical electronics or processor board. It can be operated at a certain constant power in W or be controlled to a certain temperature in °C.

In the system, the absorptive and reflective sensors may comprise a calibration heating element according to the embodiment of Figure 2.The control unit 60 may control the heating member 12, 47 to one or more predetermined body temperatures. The control unit 60 may be programmed to use the temperature sensor 11 , 45 to measure body temperature. The control unit 60 may further be programmed to use any of the absorptive and reflective sensors to measure a heat flux.

The control unit may further store temperature and heat flux values from the absorptive sensor and from the reflective sensor and temperature sensors at each of the one or more predetermined body temperatures. The control unit may further calculate a convective heat transfer coefficient and/or ambient air temperature from the convective heat flux value generated by the reflective sensor at two sensor temperatures as described in the embodiment of Figure 1 . The control unit may calculate an air velocity based on the convective heat transfer coefficient as described in the embodiment of Figure 1 . The control unit may further store for each calibration heating element a value of the surface area and resistance, and calculate a calibration heat flux for each sensor as a result of a power supplied to the calibration heating element, measuring a sensor output and determining for each sensor a sensor sensitivity on the basis of the sensor output and calibration heat flux, according to: E = U/Fo

Figure 7 shows a flowchart of a method 70 for determining an ambient air temperature and/or a convective heat transfer coefficient according to an embodiment of the present invention. The method may be carried out by a control unit such as the one of Figure 6 in the system comprising a sensor such as the one of Figure 1 or Figure 5.

In step 80 of the method, the convective heat transfer coefficient of the air Ctr is calculated based on the convective heat value, F convection, measured by the reflective sensor of the sensor 1 , 25 on a measurement side, the temperature of the body 2, 26 of the sensor is T _S en measured by the temperature sensor 11 , 45, and the ambient air temperature Tair measured by sensor 13, 46, :

Ctr ^— F convection / ( Tair “ T sen ) [1 ]

The radiative heat flux value, cpradiative, is extracted by subtracting the heat flux value measured by the reflective sensor from the heat flux value measured by the absorptive sensor. The ambient air velocity can be estimated from Ctr, using an empirical formula valid for the sensor geometry and the direction of the ambient air flow, for example by:

Vair = ((Ctr -B)/A) ² [2]

This relationship can either be empirically determined or taken from theory. A typical relationship for a single perpendicularly exposed heat flux sensor surface A = 36.7 and B = - 1 .25. For exposed surfaces at 45 ° A = 30. 0 and B = -0.78.

In step 82 the radiative temperature Trad is calculated based on

Trad ⁼ (T ⁴ sen ⁺ radiative / (e s)) ^1/4 [3]

With the Stefan-Boltzmann constant s and e the surface emissivity.

In steps 80-82 corrections may be applied for reflectivity and absorptivity not equal to 1 .

Alternatively the method may directly start at step 83 where a convective heat flux value F convection, i , F convection, 2 , measured by the reflective sensor the at 2 temperatures T _S en, t and T _S en, 20f the sensor body is used to calculate the convective heat transfer coefficient Ctr

Ctr (F convection, 2 - F convection, 1 ) / ( Tsen, 1 - Tsen, 2 )) [4] with positive heat flux from surrounding environment to the sensor, and the ambient air velocity can for example be estimated from Equation 2 above.

In step 84 of the method the ambient air temperature, Tair based on the measurement of a convective heat flux at the 2 temperatures T _S en, 1 and T _S en, 2 following: Tair T sen, 1 F convection, 1 ( T sen, 1 - T sen, 2 ) / (F convection, 2 “ F convection, 1 ) [5]

In step 85 of the method, using calibration heaters such as in the embodiment of figure 2, the absorptive and/or reflective sensors may be calibrated. For example: at a known heater surface area A, and resistance R, the heat fluxgenerated at a current I in by the heater is F = (I ² R)/ A [6]

In step 86 of the method, based on a measured sensor output U, the sensor sensitivity E is determined following: E = U / F [7]

Steps 85 and 86 of the method may be performed also prior to steps 80 to 84.