International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003 Start > Contributions >Posters > Material: Print

## Assessment of thermal conductivity of the building materials - 'Hot wire method'

Jiri Zach, Stanislav Stastnik
Institute of Technology of Building Materials and Components, Brno University of Technology, Faculty of Civil Engineering, Brno, Czech Republic

### Abstract

Non-stationary measuring equipment means a progress in methods of simple, reliable and quick determination of heat conductivity of building materials. This paper describes a new method of building materials heat conductivity coefficient determination including all involved procedures and evaluates the advantages connected with the use of this method.

### Introduction.

The thermal conductivity coefficient is the most important heat technical property of building materials - it characterizes the ability of materials to conduct heat energy.

Two groups of testing methods are used in practice for the measurement of heat conductivity as materials property:

• Stationary methods
(hot plate method, cylinder method, sphere method). These methods are quite accurate but they are time-consuming (no possibility for measuring of materials with moisture content) and the application of these method is possible only in the case of samples with exactly determined dimensions and they are very demanding concerning sample preparation.

• Non-stationary methods
- shock methods ('Hot Wire Method', 'Flash Method') utilizing secondary measuring instruments.

### The flat heat source principle

For calculations of heat transmission from flat heat source we reckon with the application of the fundamental Fourier equation for heat conduction in the form:

Let us assume that from the moment t = 0 in body plane x' heat liberation begins (j (t) = const = q). The quantity of liberated heat is r .c.q in a plane unit in a unit of time. Then the temperature in time t will be:

where: q - heat flow [W.m-2], a - thermal diffusivity [m2.s-1], t - time [s].

### The non-stationary flat (sheet) measuring equipment principle

The probe of a non stationary measuring instrument forms a semi-limited area with known parameters and a thermally sensible boundary with a flat heat source on its surface. In principle this method is based on the shock "Hot Wire Method" but in contrast with this method in substitutes the linear heat source by a flat heat source which guarantees the approximation of the measured quantity over the whole surface of the testing probe and eliminates the possible effect of local material in-homogeneities.

 Fig 1: Scheme of the assumed probe model of non-stationary flat measuring equipment for heat conduc-tivity determination of build-ing materials.

The temperature is on the measured boundary monitored by means of a reference thermocouple battery. The induced voltage is amplified by means of an AD converter and read in digital form by a PC unit. The measured values are here stored and evaluated. The output of the heat source is controlled with the help of software to secure the optimum heat development on the boundary between the probe and the tested material following the heat-technical parameters of the tested sample. For the output voltage U [V] and the value of heat conduction coefficient of the tested sample l [W.m-1.K-1] applies under ideal temperature development:

 Fig 2: Scheme of assumed connection of the measuring system for the non-stationary determination of heat conduction coefficient value.

When evaluating the results of thermal conductivity coefficient measurements by a non-stationary flat measuring equipment using the comparative method we generally assume the similarity of temperature course in the case of regular heating up of materials. The following graph formulates the typical temperature course under regular heating up (three stages: isotherm dwell, regular heating up and regular cooling):

 Graph 1: Course of temperature under regular heating up (logarithmic dependence).

At the beginning of the measurement the starting stationary temperature state (temperature distribution) is assumed. The measuring sensor and the sample form two half-infinite areas. They are limited by the boundary condition D t 0.

 Fig 3: Illustration of the non-stationary flat measuring equipment.

During the regular heating up of arbitrary sample the temperature/time dependence (in logarithmical scale) will have always a similar character. The linear part of the curve is parameterized by the used capacity of the flat source and by heat-insulating properties of both adjacent semi-spaces.

In general the calculation of the thermal conductivity value can be expressed by the equation:

where: l - thermal conductivity coefficient [W.m-1.K-1], a,b - constants of the measuring equipment [W.m-1.K-1],U - relative voltage on the heating coil of measuring equipment [-] (it represents the output because the probes resistance is all the time the same), tga - gradient of the line interpolated through the temperature curve [-]

The individual constants a,b are obtained by the measuring equipment calibration by means of two materials having known heat-technical properties.

By the process of measurement a relatively questionable is the optimization of the heat source output P [W] (Joulean heat), which is given by the ohmic resistance of the testing probe R [W] and the terminal voltage of the probe U[V]:

P = U2 / R

and the time of regular heating up t [s].

During practical measurements the measurement results on reference materials were applied for the selection of optimal measuring interval and optimal output of the heat source with respect to maximization of measurement results accurately and reproducibility.

 Graph 2: Example of measuring error course with a glass sample in dependence on the total time of experiment in the case of preliminary measurements.

### Determination of thermal conductivity coefficient of building materials by utilization of non-stationary flat measuring equipment

The non-stationary flat measuring equipment has thanks to its design many advantageous properties. It is possible to measure by this apparatus easily and rapidly the value of thermal conductivity coefficient in the case of any building material:

1. Measurement velocity.

2. In contrary to classical methods is this method incomparably quicker. The measurement itself lasts only some seconds and therefore it is possible (in comparison with stationary methods) to determine the value of thermal conduction coefficient in dependence on moisture of the tested sample.

3. Measurement flexibility.

4. The flat sensor offers the possibility of heat conduction coefficient determination of considerably non-homogenous materials. Demands concerning the sample dimension are in comparison with other methods substantially smaller. For these reasons it is possible to determine the heat conductivity coefficient even in parts of building products (for instance cut off samples from ceramics), because with standard test pieces the heat technical properties can strongly differ from the properties of final products.

5. Measurement accuracy.

6. As with every measuring method even in the case of non-stationary flat measuring instrument the greatest error comes from the test sample .if the surface of the test piece uneven. If the test piece surface is sufficiently even, the method provides relatively very exact results.

7. Small dimensions and the mass of the measuring system.

8. The measuring system consists of a flat probe (see fig.3), an AD-converter with an amplifier (external or internal) a PC unit (a notebook or a microcomputer can be used). Therefore we can state that in the case of properly chosen components it can be a mobile system and it can be utilized even directly in external conditions of production plants and building sites.

9. Simplify of the measuring method.

10. The whole measuring method is controlled by a software (including evaluation), and the output quantity is the heat conduction coefficient value (l).

11. The low price of the apparatus.

12. (The expected price of the whole measuring installation including the PC unit is up to 100 thousand Czech Crowns - 3,3 thousand Euro).

The measuring apparatus can thanks to its favorable properties be applied for the determination of the thermal conductivity coefficient measurement in a great diversity of materials and products as for instance:

• Cellular concrete,
• Plastic insulation materials,
• Materials from mineral fibers,
• Insulation materials on natural base,
• Fireproof heat insulating ceramics,
• Insulation materials on cellular gypsum an anhydrite base,
• Building ceramics,
• Heat insulating mortars and plaster mixtures, etc.

Most important is the use of the flat measuring equipment in special applications, where it is possible to apply to the full extent its specific favorable properties.

 Graph 3: Dependence of the heat conduction coefficient of a wood based heat insulating back fill on moisture content.

### Determination of the thermal conductivity depending on moisture

The moisture in the porous structure of building materials has a basic influence on the value of heat conduction coefficient. The problem of most laboratory methods of heat conduction coefficient determination is the very long period of measurement during which the test sample is exposed to the heat flow effect. Even in the case that the test sample is packed in a steam-proof foil during the measurement period a new allocation of moisture in the material structure takes place and the final measured value doesn't record quite objectively the real material properties under the given moisture content.

When using a non-stationary flat measuring equipment we can perform a series of measurements under different moisture content and considering the fact that the measuring period is 30 - 90 seconds the moisture in the test sample can be considered as constant.

### Determination of the thermal conduction coefficient of hydrating binder mixtures

 Fig 4: Photograph of the measuring system during the measurement.

Another typical application of the flat measuring equipment is the determination of heat conduction coefficient of hydrating binder mixtures. During the hydration significant changes of the hydrating material heat conduction value takes place. These changes are caused partly by the transformation of the unbound batch water into the structure of newly formed hydration products and further by the development and change of internal microstructure of materials (crystallization and re-crystallization processes).

The hydration of the test sample takes place in an insulating thermo-box in order to insulate the given system at least partially against external surroundings, firstly from sharp changes of external temperature (see fig. 4). The test sample was packed in a thin poly-ethylene foil, in order to prevent the batch water evaporation during measuring and to separate the test probe from the aggressive material of the binder. During the measurement it was necessary to fulfill two following conditions:

1. The temperature changes from the measuring probe must not influence the hydration course of the cement mixture. The maximum heat output of the source was limited to Pmax = 1.67 W. In view of the fact that the measuring period during which the probe is under voltage was shortened to 30 seconds, the liberated heat Qmax reached the value of approximately 50 J. As the result of simulation calculations we established that this heat of liberation on the boundary of the testing probe and of the sample can produce a maximum temperature change of D tmax = 0.05 K and this is considering the hydration heat liberation development and the heat losses quite negligible.
2. The cement mixture has to be in a stationary temperature state during the whole time of measurement. During the laboratory testing of the hydration heat development in the cement mixture we determined the maximum temperature gradient of 0.0004°C.s-1, which means that the concrete mixture temperature changes by hydration heat at the most by 0.012°C. Taking into consideration that the temperature change on the probe and sample boundary is of the order of some dozens of °C this temperature change during the measurement period is negligible.

It's evident that during the binder hydration a significant change of the heat conduction coefficient value takes place. A closer examination of the heat conduction coefficient curve course obviously shows that in the initial stage the hydration imitates with a certain phase delay the intensity course of hydration heat liberation (see graph 5).

 Graph 4: The dependence of heat conduction coefficient value on the course of cement paste hydration (CEM I 42.5R, w/c = 0.55).

 Graph 5: Course of temperature development in cement paste during hydration in isoperibolic calorimeter /te=20°C/ (CEM I 42,5R, w/c = 0.55).

### Conclusion

The non-stationary methods for the determination of the heat conduction coefficient are utilized particularly in cases where an application of the slab method cannot be applied. The lower measurement reliability is compensated especially by the quick realization of the experiment. The experiment evaluation is quick and it can be algorithmized for on-line processing by a computer.

The paper was elaborated with the support of the Research project VVZ CEZ MSM 261100008 and the Grant GACR 103/03/0839.

Assoc. Prof. Dr. Dipl Ing. Stanislav Stastnik, Dipl. Ing. Jiri Zach - University of Technology, Faculty of Civil Engineering, Institute of Technology of Building Materials and Components, Veveri 95, Brno 662 37, Czech Republic, Email: stastnik.s@fce.vutbr.cz; zach.j@fce.vutbr.cz

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