1. Heat Flux Sensors Isaac T. Leventon
Most of the many methods for measuring heat flux are based on temperature measurements on the surface or close to the surface of a solid material. Usually this involves insertion of a device either onto or into the surface, which has the potential to cause both a physical disruption and a thermal disruption of the surface.
As with any good sensor design, the goal for good measurements must be to minimize the disruption caused by the presence of the sensor. It is particularly important to understand the thermal disruption caused by the sensor because it cannot be readily visualized and because all heat flux sensors have a temperature change associated with the measurement. Consequently, wise selection of the sensor type and operating range is important for good heat flux measurements.
11/8/2018

2. Heat Flux Measurements
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Thermal management of materials and manufacturing processes
Annealing, film drying, surface processing
Heat exchangers, dryers, boilers, condensers
Fire Applications
Heat transfer as a controlling mechanism of fire phenomena
Temperature measurements are common and well accepted; however, heat flux is a quantity that is not easily sensed.
Maximizing or minimizing thermal energy transfer in many systems is crucial to their optimum performance.
Knowledge of heat transfer mechanisms in fire scenarios can be crucial to understanding and predicting fire behavior.
Lab Methods Day
11/8/2018

3. Heat Transfer Fundamentals
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Heat flux, q” [kW m-2]
Conduction involves heat transfer through solid materials. As defined by Fourier’s Law, conduction heat transfer is proportional to and in the opposite direction of the temperature gradient. In Cartesian coordinates, this takes the form:
𝜕𝑇 𝜕𝑡 =𝛼 𝜕 2 𝑇 𝜕 𝑥 𝜕 2 𝑇 𝜕 𝑦 𝜕 2 𝑇 𝜕 𝑧 2 where thermal diffusivity, α = k/ρC
k = thermal conductivity [ W m-1 K-1 ]
ρ = density [ kg m-3 ]
C = Specific Heat [J kg-1 K-1]
Measuring the temperature gradient is one of the primary methods for determining heat flux
Measuring the temperature response of a system according to the above equation is the second major means of determining heat flux. This method is significantly complicated as multidimensional effects (re: temperature gradients) are present.
Convection and Radiation are present at the surface of a material, to some extent, in nearly all cases. Often, the effects of one are intentionally minimized to isolate (and measure) the effects of the other.
Simultaneous measurements of both spatial and temporal distributions of heat flux are generally not feasible.
Convection heat transfer occurs by the same physical mechanisms as conduction; however, the fluid is free or forced to move over the material’s surface. To account for this fluid flow, a heat transfer coefficient, hconv, is typically defined. Correlations exist in the literature for a variety of idealized flow cases; for turbulent flows, this value is more difficult to define.
In fire conditions, defining this fluid temperature (Tf) can be very difficult, especially if a flame is present at the material’s surface.
Radiation heat transfer can occur in the absence of a medium for transmission of energy and thus is very different than the above described heat transfer mechanisms. Absorption and emission of radiation depend on material surface properties, which may be dependent on the wavelength and angular direction of the radiation. Many radiation sensors are coated with a high absorptivity coating to absorb all (most) incident radiation.
Because surface reradiation is proportional to T4, radiation detectors are usually cooled sufficiently for the power emitted from the detector itself to be negligible. In this case, the temperature distribution of the sensor is not important. This is a significant advantage over convection measurements where the temperature distribution on the surface has a big influence on the measurement. Keep this in mind when using a Gardon-type heat flux gauge.
Lab Methods Day
11/8/2018

4. 1D Planar Heat Flux Sensor
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Heat flux at a material surface (of known thermal conductivity) can be found if the temperature gradient at that position can be determined. It is extremely difficult to position thermocouples with the required spatial accuracy within the sample and thus a sensor is typically either applied on the material’s surface or mounted in a hole in the material. Ideally, δ will be as small as possible and k as high as possible to maximize the response time of the sensor; however, the above equations indicate that a decrease in δ will lead to a corresponding reduction in gauge sensitivity.
Thermocouples generate their own voltage output (Seebeck, or Thermoelectric, Effect) corresponding to the temperature difference between two junctions. Consequently, they can be connected in series to form a thermopile that amplifies the output from a given temperature difference.
Using advanced printing/manufacturing techniques, thin film micro-sensors can be less than 2 μm thick, provideing response times of less than 10 μs  a frequency response above 1kHz is possible. Such sensors are capable of withstanding high temperatures and thus, with their fast response, they are useful for aerodynamic applications, combusting flows, and other high speed events (e.g. shock passage)
Lab Methods Day
11/8/2018

5. Schmidt-Boelter Gauge
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
More commonly used are Schmidt-Boelter Heat Flux Gauges which are capable of measuring mixed convection and radiation heat transfer.
Schmidt-Boelter gauges can offer high sensitivities and gauge response (voltage generated) is highly linear with respect to incident heat flux.
Lab Methods Day
11/8/2018

6. Gardon Gauge Single thermocouple pair Fairly simple construction
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Single thermocouple pair
Temperature difference from center to edge is proportional to incident heat flux
Fairly simple construction
Water cooling possible for high heat fluxes
Not suited for use with convection heat transfer
The circular foil or Gardon gage consists of a hollow cylinder of one thermocouple material with a thin foil of a second thermocouple material attached to one end. A wire of the first material is attached to the center of the foil to complete a differential thermocouple pair between the center and edge of the
foil. The body and wire are commonly made of copper with the foil typically made of constantan. Heat flux to the gage causes a radial temperature distribution along the foil as illustrated For a uniform heat flux typical of incoming radiation the center to edge temperature difference is proportional to the heat flux (neglecting heat losses down the center wire)
The output voltage of the gauge is proportional to the product of the temperature difference (To – Ts) and the thermoelectric sensitivity of the differrential thermocouple
Lab Methods Day
11/8/2018

7. Radiometers
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Separate radiation from convection using a transparent window
Total heat flux sensors can be designed to separate radiation from convection by using a transparent window (typically quartz) to eliminate convection to the sensor face.
The field of view is limited by this window and thus reduces the total flux measured by the gauge (typical radiation heat transfer view factor calculations). This viewing angle can be purposefully narrowed to provide a narrow angle radiometer
Gas purging of radiometers can be included on radiation transducers that are to be used in a sooty environment (this helps to keep the ‘window’ clean in fire environments)
MEDTHERM (a common gauge manufacturer) offers the following removable window attachments, with the standard sapphire or optional window materials, to limit the
basic transducer to measurement of radiation heat flux only.
The angle of view for the basic transducer can be limited to 150°, 120°, 90°, 60°, 30°, 15°, or 7° for narrow view angle measurements.
Lab Methods Day
11/8/2018

8. Semi-Infinite Surface Temperature Methods
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
For short exposures, material surface temperature history can define heat transfer
Assume 1D heat transfer at surface, no effect at back:
Time limit to minimize errors:
If the thermal properties of the wall material are well known along with sufficient detail about its temperature history and distribution, heat transfer can at its surface as a function of time can be determined (in principle). When using such temperature sensors, data manipulation (post-processing of the signal) is necessary to obtain heat flux
For short exposures and sufficiently thick materials, a fast-response temperature sensor providing surface temperature history measurements can provide heat flux information by assuming 1D heat transfer, normal to the material’s surface, so long as thermal effects do not reach the material’s back surface.
Surface temperature can be measured using point measurements or spatially resolved optical measurements.
Thermocouples
• Coaxial thermocouples can be used for surface temperature measurement under high heat flux conditions (e.g. shock waves). These sensors have one TC wire inside of the second, separated by an insulating layer. One end is mounted inside of a metal sheath such that it can be pressed into a material’s surface during testing.
Resistance Temperature Detectors (RTDs) can be used to measure temperature by correlating the resistance of the RTD element with a temperature. Most RTD elements consist of a length of fine coiled wire wrapped around a ceramic or glass core. The element is often placed inside a sheathed probe to protect it (from breaking). The RTD element is made from a pure material whose resistance at various temperatures has been documented. The material has a predictable change in resistance as the temperature changes; it is this predictable change that is used to determine temperature.
• Highly accurate, relatively immune to electrical noise (hooray for industrial applications)
• RTD Sensors can be less than 0.1 μm thick, yielding extremely fast (<1 μs) response times
• Multiple configurations (compact elements, flat surface elements, RTD probes)
Thermal imaging (e.g. infrared camera) of the material’s surface can provide accurate, spatially resolved measurements of surface temperature assuming material surface emissivity is known. Careful calibration of such measurements is necessary as measurements may appear qualitatively correct despite significant inaccuracies. Such techniques can be aided by applying a highly absorptive (very dark black) coating to the material’s surface to provide the surface a high, and well-characterized emissivity.
Lab Methods Day
11/8/2018

9. Calorimeter Methods
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Determine q” by measuring amount absorbed energy, assume uniform temperature
Slug Calorimeter
Thin Skin Calorimeter
Thin metal plate welded to a thermocouple, calculate heat transfer rate (convection and/or radiation) assuming 1D heat flow
Here, Thermal Capacitance (C) is the product of the mass of the sensor and its specific heat and the ‘slug’s’ surface area is represented by A. With knowledge of the temperature response of the system, the time constant, τ, can be used here to determine a heat transfer coefficient, h. This is a really simple device to use, but it is often difficult to obtain reliable results because of heat losses and non-uniform temperatures.
Net heat flow into the thin skin calorimeter, q”net, is equal to the energy rise of the calorimeter:
q”net = ρCpδ dT/dt
Where δ is the calorimeter thickness
Weld a thermocouple to the back of the calorimeter, measure rate of temperature rise at the back of the calorimeter when exposed to fire (or other heat transfer conditions):
q”net = q”cond,fl +q”rad,ext – q”rerad – q”cond,losses
If well insulated at back and sides:
q”net = h (Tfl – Tsurf) +εσ [(Tfl)4 - (Tsurf)4 ]
Lab Methods Day
11/8/2018

10. Mounting Considerations- Physical Impacts on Flow
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Sensor protrusion, depression, or misalignment at the surface of the material may produce a boundary layer disturbance
Greater effect in laminar systems
Difficult to quantify or observe
Blowing effect
Performance and Modeling of Heat Flux Sensors – Holmberg and Womeldorf Indicate that Schmidt-Boelter heat flux gauges perform well in mixed convection/radiation (low-speed oven wind tunnel) environments with detector response in such flow conditions correlating well with the manufacturer’s suggested calibration curve.
Lab Methods Day
11/8/2018

11. Mounting Considerations- Thermal Impacts on Flow
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Under fire conditions, measured cold gauge heat flow is typically greater than net heat transfer into a sample
Water cooled sensors may alter the local temperature gradient in the flow
Assuming the gauge and material have the same surface emissivity, the net heat flux into the material can be determined from the cold surface heat flux as
“It was concluded by the Fire Research Station (UK) that smaller gauges provided less cooling of the convective boundary layer before it contacted the sensing area and thus yielded higher signals.”
Even a bare heat flux gauge will exchange heat with its surroundings by both radiation and buoyancy induced flow if its surface temperature differs from that of its surroundings. This is especially true for gauges embedded in materials that are burning or those used in enclosure fire scenarios..
Lab Methods Day
11/8/2018

12. Gauge Care and Maintenance
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Do not overheat sensors
Check water flow, if used for cooling, before each test
Ensure water is off at end of day
Using water >65°C to cool a gauge may limit formation of deposits at its surface
Protect your sensors – avoid dirt, oils, scratches, dust, and physical damage of the gauge face
Each sensor will have a different working range; exposing the gauge, or allowing it to heat above, temperatures greater than this working limit can destroy it. Your gauge manufacturer will provide more detailed specifications (call them and ask if you are unsure) but a reasonable upper limit for a Schmidt-Boelter or Gardon Gauge is on the order of 200°C. Water cooling helps ensure that such elevated temperatures are not reached.
Always ensure that water is running through a water cooled heat flux sensor while in use. Never leave the lab for the night without ensuring that this water supply is turned off.
Coaxial thermocouples typically have a higher upper temperature limit though different types are suitable only within their specific working range.
Vatell offers heat flux microsensors capable of reaching between 350 and 800°C
Some ceramic units are available for operation above °C, but accuracy may be limited.
Lab Methods Day
11/8/2018

13. Calibration
Heat Flux Measurement Heat Transfer Fundamentals Spatial Temperature Gradient Heat Flux Sensors Schmidt-Boelter Gardon Time Temperature Change Heat Flux Sensors Semi-Infinite Surface Temperature Methods Calorimeters Practical Considerations & Key Concerns for Use Calibration
Heat flux sensors should be calibrated under similar conditions as their intended use
The typical calibration is given as sensor voltage versus incident radiation
NIST Heat Flux Sensor Calibration (Blackbody radiation calibration)
When should calibrate your gauge? Many factors affect this question, frequency of use, harshness of test conditions, how it’s stored and handled.. I’ll focus on Schmidt-Boelter gauges, because that’s where my experience rests. In short, a brand new gauge (or one that’s freshly painted and calibrated) will look perfectly smooth, black, and clean. Whenever its front surface begins to deviate from this ideal, you might want to consider recalibrating it. Every 3-4 months we will recalibrate our cone calorimeter heat flux gauge versus a standard reference, even if it’s surface remains fairly clean as it is primarily used for setting of the cone heater.
‘Officially’ any time dirt, oils, dust, soot, or anything else makes contact or sticks to the gauge face, it is recommended that you calibrate it. Don’t touch the surface of your heat flux sensor by hand, don’t drop or scratch it, just be careful. That said, following non invasive testing (far field radiation) or clean burning flames where the only deposits left behind are water, we’ve had pretty good success/accuracy from our gauges.
The NIST Heat-Flux Sensor Calibration report details the specific steps they use to calibrate heat flux gauges against a blackbody source. “In
contrast to other calibration methods using temperature traceability, the objective of this calibration is to provide heat-flux traceability to NIST primary standards. This report
gives the calibration principle, the associated laboratory procedure, safety, and typical calibration results of a Schmidt-Boelter type heat-flux sensor.”
The NIST Special Publication 1031 outlines a wide range of total heat flux gauge calibration techniques employed in different fire laboratories
Such a calibration is good to keep for a standard reference gauge in your lab or for a heat flux sensor that will not need to be regularly calibrated but, in my experience, when measuring flame heat flux under fairly harsh fire conditions, you need to regularly recalibrate your gauge and, in some cases, clean, repaint, and then recalibrate the gauge entirely. In such cases, careful calibration by comparison to a reference gauge by exposing both to a range of different incident heat fluxes is sufficient. Simply:
• Support both your experimental and reference heat flux gauges such that their senor surfaces are at the same distance and orientation angle beneath a radiant heat source (e.g. cone calorimeter heater).
• Make sure water supplies are turned on
• Set the incident heat flux to a range of 3 -5 different values spanning those which you expect to measure. At each setting, once the radiant heater has reached a steady value, record the reference gauge heat flux measurement and the output voltage of your experimental gauge
• plot q”reference vs. Vexperimental ; you should have a very linear fit. The slope of the best fit line through these points is a calibration constant (kW m-2 mV-2) which relates your experimental heat flux gauges output voltage to heat flux incident on its surface. The inverse of this calibration constant is known as the gauge’s ‘Sensitivity’. A greater sensitivity is ideal as it suggests the gauge measures/senses/outputs a higher voltage for smaller incident heat fluxes (thus making its signal easier to detect)
• Turn off your heater, move your gauges to the side carefully, shut off water flow before leaving the lab.
Lab Methods Day
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14. References to consider
Heat Flux Measurement
Heat Transfer Fundamentals
Spatial Temperature Gradient Heat Flux Sensors
Schmidt-Boelter
Gardon
Time Temperature Change Heat Flux Sensors
Semi-Infinite Surface Temperature Methods
Calorimeters
Practical Considerations & Key Concerns for Use
Calibration
Heat Flux, T. E. Diller
Low Heat Flux Measurements: Some Precautions, A.F. Robertson and T.J. Ohlemiller (NIST)
High Temperature Heat Flux Measurements, Hager et. al (NIST)
Performance and Modeling of Heat Flux sensors in Different Environments, D.G. Holmberg and C.A. Womeldorf (NIST)
Narrow Angle Wide Spectral Range Radiometer Design, W. Camperchioli (NASA)
HEAT FLUX TRANSDUCERS and INFRARED RADIOMETERS for the DIRECT MEASUREMENT OF HEAT TRANSFER RATES (Medtherm)
NIST Measurement Services: Heat-Flux Sensor Calibration, Tsai et al. (NIST Special Publication )
The Resistance Temperature Detector (Omega)
Presentation/Conference Name
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15. Presentation/Conference Name
Additional equations
Analytical solution of sampled temperature data to recreate heat flux signals
Presentation/Conference Name
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