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# Physikalisch-Technische Bundesanstalt

StructureDiv. 88.4 Mathematical Modelling and Data Analysis8.41 Mathematical Modelling and Simulation > Transient methods for identifying thermal transport properties
Transient methods for identifying thermal transport properties
Working Group 8.41

The knowledge of  the thermal transport properties of different materials including natural materials has gained importance for many fields of engineering such as, for example, the building industry. The further development of transient techniques for the rapid determination of thermal properties according to transient techniques is the topic of a cooperation with the working group 1.74 “Thermal Conductivity”.

As direct measurements are not feasible, thermal conductivity and thermal diffusivity have to be determined by measurement of related quantities. A subsequent data analysis solves an inverse problem of parameter identification in heat conduction problems (parabolic differential equation). The fundamental prerequisite for handling the inverse problem consists in solving the forward problem, i.e. the numerical simulation of the experiment based on a realistic model (“virtual experiment”). This is realized by the finite element method (FEM). The inverse part is formulated as output least-squares problem and solved by the Levenberg-Marquardt algorithm.

Independent of the data analysis for indirect measurements virtual experiments have their
own importance in different levels of process development, e.g.

• determination of dependencies, e.g. material properties, cause and effect analysis, case studies with given parameters
• optimization of measuring methods, design of technical constructions or parts of them
• simulation of experiments, prediction and validation
• estimation of the permissible measuring interval
• determination of the portion of measurement uncertainty caused by the data analysis

### Example 1

The short movie below shows the FEM-simulated heat propagation for the hot strip technique calculated for symmetric reasons for a quarter of a two layered sample (axis of symmetry: left and bottom). The hot strip acts as heat source and is located centrally inside the sample, i.e. bottom left in the movie.

An algorithm was developed to identify the thermal properties of layered composites. In this way, a single measurement allows the determination of the thermal diffusivity and thermal conductivity of both materials.

### Example 2

The figure below shows the result  of the identification procedure for an air brick. λi and ai denote the thermal conductivity  and diffusivity of the i-th layer, i=1,2.

### References

• R. Model, W. Stosch, U. Hammerschmidt (2007). Virtual experiment  design for the transient hot-bridge sensor. Int. J. Thermophys. , DOI 10.1007/s10765-007-0152-8, online first.
• U. Hammerschmidt, V. Meier, R. Model (2006). New transient hot bridge sensor to measure the thermal conductivity. Therm. Conduct.   28, 278-287.
• U. Hammerschmidt, V. Meier, R. Model (2006). JANUS: High temperature transient hot bridge sensor. Therm. Conduct. 28, 288-297.
• R. Model, R. Stosch, U. Hammerschmidt (2006). Improved transient hot strip sensor design by means of FEM simulations. Therm. Conduct. 28, 298-308.
• R. Model, U. Hammerschmidt (2005). An identification procedure for thermal transport properties of layered solids by means of transient measurements. In "Thermal Conductivity 26 / Thermal Expansion 14 ", eds. R.B. Dinwiddie, R. Mannello, 346-357, DEStech Publications Lancaster, Pennsylvania.
• R. Model (2005). Thermal Transport Properties of Layered Materials: Identification by a new Numerical Algorithm for Transient Measurements. Int. J. Thermophys. 26,  165-178
• R. Model, R. Stosch, U. Hammerschmidt (2005). The virtual experiment design: Optimizing of the transient hot bridge sensor. Proc. 17th Europ. Conf. on Thermophys. Prop. .
• V. Meier, U. Hammerschmidt, R. Stosch, and R. Model (2003). A New End-effect-free Sensor for the Transient Hot Strip Technique.   Fifteenth Symposium on Thermophysical Properties, Boulder, CO, USA.
• R. Model, U. Hammerschmidt (2003). Limits and potentials of the transient hot strip (THS) method for identifying thermal properties of layered composites. High Temp. – High Press.  34,  649-655.
• R. Model (2003). Thermal transport properties of layered composites by transient measurement: Identification by a new numerical algorithm. In Proc. Fifteenth Symposium on Thermophysical Properties, Boulder, CO, USA.
• R. Model, U. Hammerschmidt (2002). Limits and potentials of the transient hot strip (THS) method for identifying thermal properties of layered composites. In Proc. “European Conference on Thermophysical Properties” , London.
• R. Model, U. Hammerschmidt (2000). N umerical methods for the determination of thermal properties by means of transient measurements . In "Advanced Computational Methods in Heat Transfer VI", eds.  B. Suden, C.A. Brebbia, 407-416,  WIT Press, Southampton, Boston.

## Contact

Physikalisch-Technische Bundesanstalt
Working Group 8.41 Modelling and Simulation
Abbestr. 2-12
10587 Berlin
Germany

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