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 OJCM  Vol.7 No.2 , April 2017
Measurement of the In-Plane Thermal Conductivity of Long Fiber Composites by Inverse Analysis
Abstract: In the present work, inverse thermal analysis of heat conduction is carried out to estimate the in-plane thermal conductivity of composites. Numerical simulations were performed to determine the optimal configuration of the heating system to ensure a unidirectional heat transfer in the composite sample. Composite plates made of unsaturated polyester resin and unidirectional glass fibers were fabricated by injection to validate the methodology. A heating and cooling cycle is applied at the bottom and top surfaces of the sample. The thermal conductivity can be deduced from transient temperature measurements given by thermocouples positioned at three chosen locations along the fibers direction. The inverse analysis algorithm is initiated by solving the direct problem defined by the one-dimensional transient heat conduction equation using a first estimate of thermal conductivity. The integral in time of the square distance between the measured and predicted values is the criterion minimized in the inverse analysis algorithm. Finally, the evolution of the in-plane composite thermal conductivity can be deduced from the experimental results by the rule of mixture.
Cite this paper: Assaf, B. , Sobotka, V. and Trochu, F. (2017) Measurement of the In-Plane Thermal Conductivity of Long Fiber Composites by Inverse Analysis. Open Journal of Composite Materials, 7, 85-98. doi: 10.4236/ojcm.2017.72005.
References

[1]   Assaf, B., Menge, H., Sobotka, V. and Trochu, F. (2005) Development of a Characterization Mold to Measure the Transverse Thermal Conductivity of a Composite Material by Inverse Analysis. Journal of Reinforced Plastics and Composites, 24, 1837-1854.
https://doi.org/10.1177/0731684405052808

[2]   Tardif, X., Agazzi, A., Sobotka, V., Boyard, N., Jarny, Y. and Delaunay, D. (2012) A Multifunctional Device to Determine Specific Volume, Thermal Conductivity and Crystallization Kinetics of Semi-Crystalline Polymers. Polymer Testing, 31, 819- 827.
https://doi.org/10.1016/j.polymertesting.2012.05.008

[3]   Villiere, M., Lecointe, D., Sobotka, V., Boyard, N. and Delaunay, D. (2013) Experimental Determination and Modeling of Thermal Conductivity Tensor of Carbon/Epoxy Composite. Composites Part A: Applied Science and Manufacturing, 46, 60-68.
https://doi.org/10.1016/j.compositesa.2012.10.012

[4]   Goodson, K.E. and Flik, M.I. (1994) Solid Layer Thermal-Conductivity Measurement Techniques. Applied Mechanics Reviews, 47, 101.
https://doi.org/10.1115/1.3111073

[5]   Rides, M., Morikawa, J., Halldahl, L., Hay, B., Lobo, H., Dawson, A. and Allen, C. (2009) Intercomparison of Thermal Conductivity and Thermal Diffusivity Methods for Plastics. Polymer Testing, 28, 480-489.
https://doi.org/10.1016/j.polymertesting.2009.03.002

[6]   Wakeham, W.A. and Assael, M.J. (1999) Thermal Conductivity Measurement. In: Webster, J.G., Ed., Instrumentation and Sensors Handbook, CRC Press, Boca Raton, Florida.
https://doi.org/10.1201/9780415876179.ch33

[7]   ASTM E1530-06, Standard Test Method for Evaluating the Resistance to Thermal Transmission of Materials by Guarded Heat Flow Meter Technique.

[8]   Norme ISO 8894-1, Matériaux réfractaires—Détermination de la conductivité ther- mique, 1984.

[9]   Hay, B., Filtz, J.R., Hameury, J. and Rongione, L. (2005) Uncertainty of Thermal Diffusivity Measurements by Laser Flash Method. International Journal of Thermophysics, 26, 1883-1898.
https://doi.org/10.1007/s10765-005-8603-6

[10]   ISO 22007-4:2008—Plastics—Determination of Thermal Conductivity and Thermal Diffusivity—Part 4: Laser Flash Method (2014).
http://www.iso.org/iso/catalogue_detail.htm?csnumber=42047

[11]   Gustavsson, M., Karawacki, E. and Gustafsson, S.E. (1994) Thermal Conductivity, Thermal Diffusitvity and Specific Heat of Thin Samples from Transient Measurement with Hot Disk Sensors. Review of Scientific Instruments, 65, 3856.
https://doi.org/10.1063/1.1145178

[12]   ISO 22007-2:2008—Plastics—Determination of thermal Conductivity and Thermal Diffusivity—Part 2: Transient Plane Heat Source (Hot Disc) Method.
http://www.iso.org/iso/catalogue_detail.htm

[13]   Shen, B., Zeng, Z., Lin, C. and Hu, Z. (2013) Thermal Conductivity Measurement of Amorphous Si/SiGe Multilayer Films by 3 Omega Method. International Journal of Thermal Sciences, 66, 19-23.
https://doi.org/10.1016/j.ijthermalsci.2012.10.022

[14]   Hashimoto, T., Morikawa, J., Kurihara, T. and Tsuji, T. (1997) Frequency Dependent Thermal Diffusivity of Polymers by Temperature Wave Analysis. Thermochimica Acta, 304-305, 151-156.
https://doi.org/10.1016/S0040-6031(97)00026-9

[15]   ESI-Group. PAM-RTM Simulation Software of the Resin Transfer Molding (RTM) Process.
https://www.esi-group.com/

[16]   Chen, H., Ginzburg, V.V., Yang, J., Yang, Y., Liu, W., Huang, Y., Du, L. and Chen, B. (2016) Thermal Conductivity of Polymer-Based Composites: Fundamentals and Applications. Progress in Polymer Science, 59, 41-85.
https://doi.org/10.1016/j.progpolymsci.2016.03.001

[17]   Woodbury, K.A. and Jarny, Y. (2003) Inverse Engineering Handbook—The Adjoint Method to Compute the Numerical Solutions of Inverse Problems. C. Press LLC.

 
 
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