Sensor and method for measuring a deposit in a fluid duct

The sensor device with transient temperature recording addresses the limitations of steady-state methods by providing rapid, energy-efficient, and localized fouling detection in fluid ducts, enhancing accuracy and robustness.

WO2026153742A1PCT designated stage Publication Date: 2026-07-23TOPERFORM SENSOR BV
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Patent Information

Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
TOPERFORM SENSOR BV
Filing Date
2025-12-18
Publication Date
2026-07-23

AI Technical Summary

Technical Problem

Existing sensors for measuring deposits in fluid ducts are slow, energy-intensive, and sensitive to lateral heat transport, requiring thermal guards and affecting the fluid flow, with measurements being less accurate due to reliance on steady-state methods.

Method used

A sensor device with a separate heating element and temperature sensor on a flexible carrier, allowing transient temperature recording during heating and cooling phases, providing a richer dataset for accurate fouling detection and minimizing energy input.

Benefits of technology

Enables rapid, energy-efficient, and localized fouling detection with reduced interference in fluid flow, offering improved accuracy and robustness against noise and process variations.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to a sensor device (1) for measuring a deposit (14) on a wall, such as the wall of an elongate fluid transport channel (12). The sensor device (1) has carrier, that may be a strip-shaped carrier (2) of a flexible film material, a heating element (3) and at least one temperature sensor (s1, s2) being placed on the carrier (2). The carrier is adapted to be placed with the heating element (3) and the at least one temperature sensor (s1, s2) in heat conducting contact with a planar or cylindrical exterior surface of the wall. The sensor is adapted to provide temperature values at time intervals during heating up when the heating element (3) is active and during cooling down when power to the heating element is reduced or switched off.
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Description

[0001] P138616PC00

[0002] Title: Sensor and method for measuring a deposit in a fluid duct

[0003] Technical Field

[0004] The invention relates to a sensor device for measuring a deposit, such as in a fluid duct, the sensor device comprising a heating element and at least one temperature sensor. The invention also relates to a method for measuring the presence and / or the thickness of a deposit, in particular in a fluid duct.

[0005] Background

[0006] In US 6,499,876 a measurement method is described for determining the presence of deposits in a milk conduit by supplying a heat flux to the conduit and measuring the gradient of the wall temperature associated with this heat flux.

[0007] EP 1 989 530 Bl describes a plate-type heat exchanger with a heating resistor placed on an end plate of the heat exchanger. A thermocouple is used to measure the temperature in the immediate vicinity of the resistor to detect the formation of a scale deposit. The heating resistor and thermocouple are placed on a flexible carrier and are covered by an insulating layer to direct the heat flux that is supplied by the resistor into the fluid channel.

[0008] EP 4 390 371 Al describes a flexible sensor for measuring the thickness of a deposit layer in a duct. The sensor comprises a resistive heating element made of a PTC material. When power is provided to the resistor it heats up to a steady state, at which moment the temperature of the resistor is deduced from the its resistance value so that it acts as a sensor. The resistance is determined by measurement of the current and the voltage that are supplied.

[0009] The known sensor and measurement method have as a disadvantage that temperature measurements can only start after reaching a steady state, so that the known method is relatively slow. The known measurement method furthermore is relatively sensitive to lateral heat transport and special thermal guards need to be applied to prevent later heat diffusion. Furthermore, the known method inputs a relatively large amount of energy into the wall of the duct, which may have an adverse effect of the substance flowing through the duct.It is an object of the invention to provide a sensor and a measurement method for accurately determining the formation of a deposit layer on variety of surfaces, such as in a vessel or in a duct. It is another object to provide a sensor and measurement method that allow rapid measurements and that utilize relatively low amounts of energy and to prevent the impact on formation of deposits by the measurement. It is a further object to provide a sensor that can be easily applied to a variety of surfaces, in particular conduits, of different geometries.

[0010] Summary

[0011] According to the invention, a sensor device is provided for measuring a deposit on a wall comprising a heating element and at least one temperature sensor being placed on the carrier, the carrier being adapted to be placed with the heating element and the at least one temperature sensor in heat conducting contact with a planar or cylindrical exterior surface of the wall, the sensor being adapted to provide temperature values at time intervals during heating up when the heating element is active and during cooling down when power to the heating element is reduced or switched off. The sensor according to the invention allows full temperature development recording. The separate heating element and senor enable simultaneous independent heating and temperature measurement, allowing the full time-dependent temperature response to be captured during the entire measurement cycle, including both heating and cooling phases. This has several advantages over the known steady- state methodology.

[0012] The sensor according to the invention comprises a separate sensor and heating element and hence provides improved speed of measurement as it eliminates the need to wait for a new steady-state wall temperature, which may require extended durations depending on system dynamics. By applying a relatively short heat pulse and recording the subsequent heating and cooling phases, the transient thermal behavior can be quantified directly.

[0013] According to the invention, a richer dataset is obtained. The analysis of the complete temperature-time curve, rather than relying solely on a steady-state temperature rise, provides richer diagnostic information and a more accurate characterization of fouling and heat transfer conditions. The full transient temperature response provides substantially more information than steady- state methods.By measuring the complete heating and cooling curve, the conduction resistance (wall and fouling) and the convective resistance to the fluid can be distinguished, as different time phases are dominated by different heat transfer mechanisms (e.g., the early-time slope immediately after heater activation is conduction-dominated, while the cooling phase after power removal reflects convection strength relative to the static conduction baseline). This improved understanding eliminates the need for conduction-limiting design measures, such as thermal guards or larger heating areas.

[0014] By measuring transient features, the sensor of the present invention is also more sensitive to slight changes, enabling detection of incipient fouling layers that may not be visible in equilibrium readings.

[0015] Curve fitting or model-based inversion can be applied to a full dataset of recorded temperatures, making the analysis more robust against noise compared to relying on a single steady-state AT.

[0016] Further, the sensor according to the invention allows the use of a method inherently providing internal validation: deviations in the expected transient curve shape can indicate sensor misalignment, additional coatings on the wall, or abnormal flow conditions. Such an approach also works more reliably under unsteady process conditions, as rapid sensor responses can be distinguished from slower bulk flow or temperature drifts.

[0017] In addition, reaching a new steady-state temperature requires input of significantly more time and energy than using a relatively short heating pulse according to the invention. Hereby the sensor according to the invention avoids influencing the process of the fluid flowing through the duct as well as higher power requirements and more difficult certification.

[0018] The sensor device may comprise a strip-shaped carrier of a flexible film material having a length L and a width W, wherein L is at least 5 cm, preferably at least 10 cm and L / W >= 3. The relatively small strip shaped sensor of the invention adds reduced amounts of energy to the stream. When the fouling sensor is operated to achieve a given wall temperature rise (AT) at the sensing location (resolution of the sensor) of the measurement system, the total heat supplied to the process stream is proportional to the heated surface area. Accordingly, a larger heated patch requires a greater overall heat input than a smaller heater to reach the same AT at the measurement point. This has several effects.Firstly, an increased amount of energy dissipated in the sensor alters the thermal state of a larger volume of the process fluid, thereby exerting a stronger influence on the process itself. Such influence can limit the usability of the sensor in measurement systems where even modest temperature excursions promote unwanted chemical reactions. For example, in polymerization-sensitive streams, monomers such as styrene, acrylates, and vinyl chloride can undergo uncontrolled polymerization upon small temperature increases. In other cases, such as recycled plastic or heavy hydrocarbon streams, additional heat input may cause thermal decomposition or cracking reactions, leading to coke formation or other deposits. By the sensor according to the invention reducing the heated footprint, the total added energy is minimized, decreasing the likelihood of triggering such adverse reactions while enabling accurate fouling measurement.

[0019] The low energy usage of the strip-shaped sensor according to the invention reduces power requirements and improves certification possibilities: Further, additional power requirements have other adverse effects on the sensor’s usability. At reduced power it is easier to certify the sensor design under ATEX or lECEx standards.

[0020] The strip-shaped sensor of the invention improves the locality of fouling measurement (information “smearing”). The relatively small-sized rectangular, flow-aligned heater produces a more localized fouling signal because the temperature at its center reflects mainly what is happening directly underneath the strip, as the fouling measurement corresponds to an average of the thermal resistance over the entire heated area. Heat conduction within the wall of the measurement system extends laterally beyond the geometric boundary of the heater, so the temperature measured at the center is influenced not only by the fouling directly beneath it but also by regions surrounding the heated footprint. Reducing the heater area limits this averaging effect and provides a measurement that is more representative of local fouling conditions. Further, the level of fouling in a pipeline is determined in particular by the orientation of the pipeline, wherein a horizontal orientation differs from a vertical orientation, and by the diameter of the pipeline. As a result, an average fouling value is not representative, whereas a spot measurement provides more relevant information.

[0021] The strip length and orientation (flow effects) improve the accuracy of the measurements. The heating element supported on the elongated strip can be arranged with its longitudinal axis aligned parallel to the flow direction of the process fluid within the conduit. The strip is configured with a length that is greater than its width such that acentral portion of the strip, where at least one temperature sensor is located, is positioned at a sufficient distance from both the upstream and downstream edges of the heated area. This arrangement ensures that the measured wall temperature at the central portion is minimally influenced by the non-uniform convective heat transfer conditions that exist adjacent to the upstream and downstream edges of the strip, where the thermal boundary layer respectively initiates and thickens. By positioning the measurement zone within the central region of an elongated, flow-aligned strip, the sensor system provides a temperature response that more directly reflects the local fouling resistance of the fluid-contacting surface, rather than edge -induced convection effects.

[0022] The sensor may be applied to vessels or ducts. The wall may define a fluid transport channel, or form part of a vehicle, a process vessel, and the like.

[0023] By placing the carrier with the sensor and the heating element in heat-conducting contact with the outside wall surface, for instance of a fluid transport channel, heat can be injected into the channel and the uptake of injected heat by the wall can be accurately determined. The heating element and the sensor can be situated in a flat contact surface of the flexible carrier and can be placed in close contact against a flat planar or cylindrical surface of the wall of the fluid transport channel. The carrier may be adhesively attached or may be attached via a tape that is applied over the carrier, and that acts as a thermal insulation reducing heat loss to the environment.

[0024] By encircling a part of the cross-section of the fluid transport channel, good thermal contact between the sensor and the wall of the fluid transport channel, which may have a round, rectangular or a differently shaped cross-section, can be established in an easy and reliable manner. Placing the flexible carrier film against at least a part of the cross section of the channel and attaching it by covering it with a tape or by wrapping a layer of tape around the channel and the carrier as a primary form of insulation, can provide a tight compression of the sensors and the heating element against the wall surface of the fluid transport channel, and provide accurate measurement values.

[0025] With “fluid” as used herein, a flowable material such as a gas, a liquid or a powder is intended.

[0026] The sensor device according to the invention can be placed on the outside surface of fluid ducts, on an inside of a ship hull to measure the presence of fouling below the water line, onthe inside of a hull or wing of an aircraft, on the plating or window of the body of a road vehicle such as a train or car, on windows of buildings or on any flat planar, cylindrical or spherical surface on which the presence of a deposit layer needs to be detected.

[0027] In an embodiment, a position of the heating element along the length of the carrier corresponds to a position of the temperature sensor along the length of the carrier. The heating element may comprise a heating coil that surrounds the one or more temperature sensors.

[0028] The sensor device may comprise at least two temperature sensors situated near one another. The sensor signals can be compared. When a difference in signals is observed that is above a predetermined threshold level, this may form an indication of a faulty measurement.

[0029] The strip may comprise longitudinal sides and a transverse connector side, power leads of the heating element and at least one signal lead of the temperature sensor being formed by flexible conductors extending along the length of the strip to a connector element on the transverse side.

[0030] The sensor device may be attached to the fluid duct by means of an adhesive, an adhesive tape or may according to one embodiment, comprise on one side a heat conducting adhesive.

[0031] The film may be formed of a polyimide having a melting point of at least 250°C, preferably at least 300°C.

[0032] A method of measuring the thickness of a deposit layer on a wall comprises:

[0033] placing a sensor device on the outside of the wall, the sensor device comprising a carrier of a flexible film material, carrying a heating element and at least one temperature sensor;

[0034] covering the sensor device with an insulating material,

[0035] powering the heating element during a heating period,

[0036] measuring a temperature profile with the sensor during a recording period, and determining any of the parameters of the group consisting of the maximum value of the temperature profile, the area of the temperature profile and the decay rate of the cooling section of the temperature profile, for instance related to a single exponential curve fit to the cooling section, or any combination thereof.The wall may define a fluid transport channel.

[0037] The data coming from the temperature sensor can be analyzed using artificial intelligence(AI) to predict the formation of a deposit or contamination layer. The sensor device may be connected via loT techniques to a data platform for data analysis. From the area under the observed temperature graph, the peak value of the temperature gradient and / or the decay rate of the cooling section of the temperature profile , the thickness of a deposit layer can be accurately determined.

[0038] Brief Description of the Drawings

[0039] Some embodiments of a sensor device and measuring system and method according to the invention will, by way of non-limiting example, be described in detail with reference to the accompanying drawings. In the drawings:

[0040] Fig. 1 shows a perspective view of a sensor device according to the invention,

[0041] Fig. 2 shows a schematic cross section of a sensor device placed on a fluid transport duct, Fig. 3 shows a cross-sectional view of a fluid transport duct and a sensor device according to the invention,

[0042] Fig. 4 shows sensor device wrapped around a duct,

[0043] Fig. 5 shows a graph of temperature readings taken with a sensor device according to the invention,

[0044] Fig. 6 shows a comparison of temperature readings with and without a deposit layer formed on the inside wall of the fluid transport duct, and

[0045] Fig. 7 shows a web-based measurement system including sensor devices according to the invention.

[0046] Detailed Description

[0047] Figure 1 shows a sensor device 1 comprising a strip-shaped carrier 2 with longitudinal sides 9, 9’, and transverse sides 10, 10’. The carrier 2 comprises a measurement section 2a and a connector section 2b. The measurement section 2a is provided with a heating element 3 and two temperature sensors SI, S2. The sensors SI, S2 may each comprise for instance a PT1000 Resistance Temperature Detector (RTD), having an accuracy of 0, 1°C. The heating element may comprise a coil 3 with a power of 0- 80W, for instance 15W or 30W.The sensors SI, S2 are connected to flat cable connector 4 at a connector side 10 of the carrier 2, via flexible conducting signal lines 5, 6 that extend along the measurement section 2b of the carrier. The conductors 5, 6 can be formed by airs of metal stri s. The coil 3 is connected to the cable connector 4 via conductor leads 7, 8. Two resistors Rl, R2 are included in the signal lines 5, 6 of the sensors SI, S2 for providing proper read out of the sensor device 1 and are tuned to the length of the cable that attaches to the connector 4.

[0048] The sensor device 1 has a measurement section 2a of length LI which provides the measurement surface that is brought into contact with the fluid transport channel, and which may be of a length of for instance 10 cm. The connector section 2b of the sensor device 1 with a length L2 can extend from the fluid transport channel to a controller and may have a length of 15-40 cm. The width W of the sensor may be 1-10 cm, for instance 2.5 cm.

[0049] The carrier 2 may be formed of a heat-resistant flexible film material such as polyamide with a melting point of 300°C and having a thickness of 1mm. The conductors of the leads 7,8 and the signal lines 5,6 may be formed by copper strips of a thickness of 0,01-0,05 mm that have been adhesively connected to the film material.

[0050] Figure 2 schematically shows the sensor device 1 with the carrier strip 2 attached to the outside wall surface of a conduit 12 transporting a fluid in the flow direction of the arrow 13. A control unit 11 provides power to the heating coil through the leads 7, 8 to input heat into the flow of the fluid. The control unit 11 may control the supply of up to 20W to the heating element 3, increasing in steps of 0.1 W.

[0051] The signal leads 5, 6 provide temperature measurement signals from the sensors SI, S2 to the control unit 11, such as a change in resistance value of the sensors. On the basis of the temperature measurements, which may comprise taking a temperature reading every 200 ms-500 ms, the control unit 11 can detect the presence and / or the thickness of a layer 14 of fouling deposit on the inside of the wall of the conduit 12.

[0052] Figure 3 shows a cross-sectional view of the conduit 12, with a carrier strip 2 extending around half the circumference of the conduit. An insulating layer 15 is provided to overlie the measurement surface of the carrier strip 2 to prevent loss of heat to the environment outside of the conduit 12. The carrier strip 2 may be adhesively connected to the outer surface of the conduit 12. The strip may be provided with an adhesive layer, covered by a releasable backing that is removed when the strip is mounted in position. The insulating layer may be wrappedaround the circumference of the conduit 12 or may extend along a part of the circumference and may be adhesively attached the outward facing surface of the carrier strip 2.

[0053] Figure 4 shows the sensor device 1 with the measurement section 2a wrapped several times around the conduit 12. The connector section 2b extends to a housing 17 of the control unit 11, where the connector 4 attaches to a printed circuit board carrying a processor 18 and a memory 19. The control unit 11 may be connected to a network via a cable 20.

[0054] Figure 5 shows a set of temperature measurements from the sensors SI, S2 taking temperature readings during a measurement time Tm of 100s, wherein heat is supplied to the conduit by the heating element 3 during a heating time Th. The temperature readings are taken at intervals of 200 ms and stored in the memory 9 of the control unit 11.

[0055] The height / amplitude H of the temperature curve is the maximum temperature that is reached just after switching off the power input to the heating element 3. The height is determined by the amount of energy that is supplied and will increase when an insulating fouling deposit layer is present on the inside wall of the duct.

[0056] The decay rate D related to a single exponential curve fit to the cooling section of the curve shows how efficiently the object cools. The presence of a fouling deposit decreases the convective heat transfer occurring via the fluid in the pipe. Larger values of D mean faster cooling, while smaller values indicate slower cooling, therefore, serving as a measure of the degree of fouling.

[0057] The surface areas al and a2 during heating up and during cooling down provide a measure for the energy that is taken up by the conduit wall. An increase in the thickness of the deposit layer will result in an increase in insulation of the conduit wall which contains more energy at the conduit wall and hence results in a larger surface area.

[0058] The heigh H, the decay rate D, and the surface areas al, a2 below the temperature curve may be determined by the processor 18 and are correlated to the presence and / or thickness of a deposit layer 14 on the inside wall of the fluid conduit 12. Based on the values of H, B and / or al and a2, and a comparison of these values with measurements of a clean duct without a fouling deposit layer, as shown in figure 6, the control unit 11 may output a value of the thickness of a deposit layer or may provide a visual or audible indicator of the presence of deposit layer.In order to obtain a good resolution at the sensor, i.e., a larger difference in energy uptake in case of the presence of a deposit layer, a liquid flow should be present in the conduit. The liquid flow is also important for dissipation of the heat that is supplied, so that measurements can be taken in rapid succession.

[0059] A change in flow rate and in liquid temperature does not negatively affect the measurements and can be filtered out by carrying out a simultaneous background measurement in which first no energy is supplied, and instead only the temperature of the fluid in the conduit is measured, so that variations in the temperature and flow may be accounted for. This measurement can be conducted using the same hardware as the actual measurements of the fouling layer. In this manner the influence of measurement errors and the effects of variations in flow rate and temperature on the measurement of the thickness of the deposit layer can be minimized.

[0060] Figure 7 shows a number of control units 11, gateways 25 and a cloud platform 30 for sending measurement data to the cloud 31, and for receiving remote instructions for the control units 11.

[0061] Each gateway 25 may schedule up to 8 control units 11 and sets up a bi-directional communication with the cloud 31. In case the communication to a gateway 25 via the cloud 31 is interrupted, the gateway may continue to function in a standalone manner, and store measurement data supplied by the control units 11 in a buffer memory . The control units 11 may be provided with a memory, for instance on an SD card. When connection is reestablished, the commands that have been sent to the gateway 25 are processed and the measurement data are sent to the platform 30. When no measurements for determining the thickness of a deposit layer are taken, the gateways 25 may provide temperature readings taken by the sensors to the platform 30.

[0062] The control units 11 and sensor hardware in the field may communicate via loT technologies (4G) over the cloud platform 30, where the data can be stored in a secure environment. Via such secured environment, the user can interpret the data through a dashboard. In a programming module, calculations can be made on the data for interpretation or for instructing a digital twin model.

[0063] The platform 30 has as functionalities:

[0064] Communication with the sensors and the control units 11 in the field, Managing the firmware and software of the sensors and control units 11 in the field, Representing the acquired data through one or more dashboards,Managing the signal quality and detection of anomalies in measurement conditions, as well as making predictions about soiling by deposit formation.

[0065] Communication with the gateways 25 may be established through a MQTT server 32, providing a standards-based messaging protocol for machine-machine communication and loT applications. The MQTT server 32 receives input from a management application 33. A relational database 34, for instance an open-source object-relational database system as PostgreSQL, can be connected to the management application 33.

[0066] Access to the database 34 is provided through an authentication application 35, for instance Keycloak.

[0067] The data supplied by the MQTT server 32 may be provided to a streaming platform 37 for data stream processing, real time pipelines, and data integration at scale. Metadata, such as apparatus status, may be exchanged between the management application 33 and the streaming platform 37. The platform 37 may comprise an open source distributed streaming system such as Kafka.

[0068] The streaming platform 37 may connect to a time-series data processing application 39 for real-time processing of the data for analysis and for discovering trends. The application 39 may for instance comprise Timeseries DB Clickhouse.

[0069] The platform 37 may input into an application 40 for providing analytics and interactive visualization through charts, graphs, or dashboards. The application 40 may for instance comprise Grafana.

[0070] In an application 41, the data from the time-series application 39 may be processed, modelled, and analyzed. Open-source software Jupyter may be used for the application 41.

Claims

Claims1. Sensor device (1) for measuring a deposit (14) on a wall, the sensor device (1) comprising a carrier (2) of a flexible film material characterized in a heating element (3) and at least one temperature sensor (si, s2) being placed on the carrier (2), the carrier being adapted to be placed with the heating element (3) and the at least one temperature sensor (si, s2) in heat conducting contact with a planar or cylindrical exterior surface of the wall, the sensor being adapted to provide temperature values at time intervals during heating up when the heating element (3) is active and during cooling down when power to the heating element is reduced or switched off.

2. Sensor device (1) according to claim 1, wherein the carrier (2) is strip-shaped having a length L and a width W, wherein L is at least 5v cm, preferably at least 10 cm and L / W > =3.

3. Sensor device (1) according to claim 1 or 2, wherein the wall defines a fluid transport channel (12), the carrier (2) being adapted to extend along a circumferential direction or a length direction of the transport channel (12) or to encircle at least 75% of a cross-section of the transport channel (12) and preferably to encircle the cross section of the transport channel (12) at least once, more preferably at least twice.

4. Sensor device (1) according to any of claims 1 -3, a position of the heating element (3) along the length of the carrier (2) corresponding to a position of the temperature sensor (si, s2) along the length of the carrier.

5. Sensor device (1) according to any of claims claim 1- 4 comprising at least two temperature sensors (si, s2) situated near one another.

6. Sensor device (1) according to any of the preceding claims, the strip-shaped carrier (2) comprising longitudinal sides (9, 9 ) and a transverse connector side (10), power leads (7, 8) of the heating element (3) and at least one signal lead (5, 6) of the temperature sensor (si, s2) being formed by flexible conductors extending along a length L2 of the carrier (2) to a connector element (4) at the transverse connector side (10).

7. Sensor device (1) according to any of the preceding claims, the carrier (2) comprising on one side a heat conducting adhesive.

8. Sensor device (1) according to any of the preceding claims, the film material of the carrier (2) having a melting point of at least 150°C, preferably at least 200°C.

8. Method of measuring the presence and / or the thickness of a deposit layer (14) on a wall, such as on the inside of a fluid transport channel (12), the method comprisingplacing a sensor device (1) on the outside of the wall, the sensor device comprising a carrier (2) of a flexible film material, carrying a heating element (3) and at least one temperature sensor (si, s2);covering the sensor device (1) with an insulating material (15),powering the heating element during a heating period (Th),measuring a temperature profile with the sensor during a recording period (Tm), determining any of the parameters of the group consisting of the maximum (H) of the temperature profile, the area (al, a2) of the temperature profile and the decay rate of the cooling section of the temperature profile, or any combination thereof.

9. Assembly of a sensor device (1) comprising a heating element (3) and at least one temperature sensor (si, s2) being placed on the carrier and a control unit (11) comprising a processor (18), the control unit (1) being connected to the sensor device (1) and being configured forpowering the heating element (3) during a heating period (Th),reading temperature values from the sensor (2) during a recording period (Tm) for determining a temperature profile, anddetermining any of the parameters of the group consisting of the maximum value (H) of the temperature profile, the area (al, a2) of the temperature profile and the decay rate of the cooling section of the temperature profile, or any combination thereof.

10. Method according to claim 8, wherein the recording period comprises a cooling down period in which power that is supplied to the heating element (3) is reduced or is switched off.

11. Assembly according to claim 9, the sensor device (1) comprising a strip-shaped carrier (2) of a flexible film material having a length L and a width W, wherein L is at least 5 cm, preferably at least 10 cm and L / W >= 3, a heating element (3) and at least one temperature sensor (si, s2) being placed on the carrier.

12. Assembly of a fluid duct (12) having an outside wall having a predetermined cross-section, and a flexible sensor device (1) comprising a strip-shaped carrier (2) of a flexible film material having a length L and a width W, wherein L is at least 5 cm, preferably at least 10 cm and L / W >= 3, a heating element (3) and at least one temperature sensor (si, s2) being placed on the carrier (2), the carrier (2) being attached with temperature sensor (si, s2) and the with the heating element (3) in heat conducting contact with the wall of the fluid duct (12), either through wrapping around the duct (12) or patchwise placement.