# R-Value Measurements and Thermal Conductance

A heat flux sensor measures heat energy per unit area transferred through a surface, and so can be used to determine the R-value, or how resistant a material is to heat flow, in situ. Compared to other methods, this is non-destructive and can provide quantitative measures of the R-value. In situ measurements are more accurate as they take into account the factors that affect thermal performance over time such as material degradation, effect of humidity, and physical damage.

FluxTeq’s PHFS product line of heat flux sensors use a differential-temperature thermopile design to measure heat flux through the sensor surface. A thermocouple integrated into the design measures temperature. PHFS-09 or PHFS-09e are highly sensitive sensors that are suitable for measuring low heat fluxes generally seen in R-value measurements.

## Theory Behind R-value Measurements

R-value is determined using Fourier’s law of conduction, which assumes steady-state one-dimensional heat transfer through the material. The schematic below shows how the PHFS heat flux sensors can be used experimentally to determine the R-value.

Figure 1. Diagram of conductive heat flow through a material and the necessary experimental setup to determine R-value of the material.

 ( 1 )

Here q” is the one-dimensional heat flux through the material, k is the thermal conductivity, and t is the thickness. From this, the R-value is calculated as:

 ( 2 )

Three unknown variables, heat flux (q”), T2,outside, and T1,inside, need to be determined to calculate the R-value. These values can be determined using 2 PHFS sensors placed on the inner and outer surface of the tested material. Note that although two PHFS sensors are not required and one surface can have only a temperature sensor, FluxTeq recommends using two to ensure that the heat flux is equal through both surfaces.

Several measurements are taken over a long time and analyzed to get the effective R-value. One possible equation for calculating the R-value is:

## Measuring Thermal Conductance (U-value)

Using the same measurements above, one can also calculate the U-value, which is the reciprocal of the R-value, and is given as:

## Standards Describing In situ R-value Measurement Practices

American Society of the International Association for Testing and Materials (ASTM) and the International Organization for Standardization (ISO) have described standard tests for in situ measurements for calculating thermal resistance using heat flux sensors. Some of them include:

. .
ASTM 1046 Standard Practice for In Situ Measurement of Heat Flux and Temperature on Building Envelope Components
ASTM 1155 Practice for Determining Thermal Resistance of Building Envelope Components from In Situ Data
ISO 9869 In situ measurement of thermal resistance and thermal transmittance
ASTM 1041 Standard Practice for In Situ Measurements of Heat Flux in Industrial Thermal Insulation Using Heat Flux Transducers

## Tips for Taking Accurate Measurements and Data Analysis

1. Avoid placing the heat flux sensor near air vents as the air flow will cause fluctuations in the sensor, leading to inaccurate measurements.
2. Placing sensors in direct sunlight may introduce errors due to solar heating. Hence, place sensors in the shade.
3. Although measurements are effective after 1 hour, it is recommended that measurements are taken for at least 48 hours.
4. Maintaining a large temperature difference of at least 10 ºC across the material for the entire test duration is recommended. The larger the temperature difference, the more accurate the measurements.

## Importance of Stable Testing Conditions

Since the equation used to measure the R-value assumes steady-state conditions, it is important to take note of any changes in the heat flux during the testing. When measuring materials with a large thermal resistance such as walls, it is important to ensure steady-state heat transfer. Achieving this may take a long time and is a function of the material thickness, location, and the thermal diffusivity of each layer of the material.

This information has been sourced, reviewed and adapted from materials provided by FluxTeq.

For more information on this source, please visit FluxTeq.

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