Development of a Characterization Mold to Measure the Transverse Thermal Conductivity of a Composite Material by Inverse Analysis

Abstract

In the present work, the transverse thermal conductivity of a composite material is determined by inverse analysis of the heat conduction phenomenon. Knowing the evolution of boundary conditions in time, i.e., the bottom and top surface temperatures of a specific sample, the thermal conductivity can be deduced from transient temperature measurements at three given positions through the thickness of the part. Starting from an initial estimate of thermal conductivity, the inverse method begins by solving the direct problem, i.e., the heat equation. The solution gives the transient temperature field everywhere in the composite sample. Calculated temperatures are then compared with transient experimental measurements based on a criterion evaluating the integral in time of the square of the distance between the measured and predicted temperatures. Conductivity is modified iteratively so as to minimize this criterion until the desired accuracy is achieved. The inverse methodology is tested in this article for a composite part made out of unsaturated polyester resin and unidirectional glass fibers. A special multifunctional mold was designed to produce the composite test plates by the Resin Transfer Molding Process (RTM) and at the same time, measure the transverse thermal conductivity as a function of time and resin degree of polymerization. The mold has an adjustable cavity depth to accommodate various experimental configurations and allows easy testing of a series of different fiber volume contents. It is equipped with controlled heating and cooling devices. Numerical simulations were performed to determine the dimensions of the mold and to optimize the positions of temperature and pressure sensors.

Keywords

inverse analysis transverse thermal conductivity mold design

Get full access to this article

View all access options for this article.

References

Yao, L. S. (1982). Heat Transfer in Porous Media, American Society of Mechanical Engineers, New York .

Giaretto, V. and Torchio, M. F. (2004). Two-Wire Solution for Measurement of the Thermal Conductivity and Specific Heat Capacity of Liquids: Experimental Design , International Journal of Thermophysics, 25(3): 679-699 .

Wakeham, W. A. and Assael, M. J. (1999). Thermal Conductivity Measurement, The Measurement, In: Webster, J. G. (ed.), Instrumentation and Sensors Handbook, CRC Press LLC, Boca Raton, FL .

Laurent, J. P. (1991). An Estimation Model for the Dry Thermal Conductivity of Autoclaved Aerated Concrete , Materials and Structures, 24(141): 221-226 .

Oms, J. L. (1991). Identification of Thermal Parameters of Reactive and Deformable Porous Medium - Gas - Solid Chemical Heat-Pumps Application , Revue Générale de Thermique, 30(354-355): 394-400 .

Degiovanni, A. , Batsale, J. C. and Maillet, D. (1996). Mesure de la Diffusivite Longitudinale de Materiaux Anisotropes: Panorama des Techniques Developpees au LEMTA , Revue Générale de Thermique, 35: 141-147 .

Jarny, Y. (2003). The Adjoint Method to Compute the Numerical Solutions of Inverse Problems, In: Woodbury, K. A. (ed.), Inverse Engineering Handbook, CRC Press LLC, Boca Raton, FL .

Richer, G. R. (1981). An Inverse Problem for the Steady State Diffusion Equation , SIAM J. Appl. Math., 41(2): 210-221 .

Cheng-Hung, H. and Jan-Yuan, Y. (1995). An Inverse Problem in Simultaneously Measuring Temperature-Dependent Thermal Conductivity and Heat Capacity , Int. J. Heat Transfer, 38(18): 3433-3441 .

10.

Menge, H. , Trochu, F. , Millischer, A. and Sobotka, V. (2002). An Experimental Device and an Inverse Method to Determine the Thermal Conductivity of a Fiber Reinforced Composite as a Function of Temperature and State of Cure , In: 4th Canada-Japan Workshop on Composites, Vancouver, Canada, Sept. 19-21.

11.

Bailleul, J.-L. , Sobotka, V. , Delaunay, D. and Jarny, Y. (2003). Inverse Algorithm for Optimal Processing of Composite Materials , Composites: Part A, 34: 695-708 .

12.

Jauffres, D. (2002). Conception d’une Presse Experimentale de Moulage de Pieces Composites par le Procede RTM Dedieea des Mesures de Conductivite Thermique, In: rapport de stage, INSA de Lyon, Éal. Polytechnique de Montre

13.

Geuzaine, C. and Remacle, J. F. (2005). GMSH “Mesh Generation Freeware”, http://www.geuz.org/gmsh

14.

PAM-RTM. (2005). Users Guide, ESI-Group, http://www.esi-group.com

15.

Sobotka, V. (2001). Determination des Parametres Thermophysiques et Cinetiques d’une Resine Polyester Insaturee, In: Rapport de Stage de Fin d’Etudes, Ecole Polytechnique Montréal. ćole

16.

17.

18.

Farmer, J. D. and Covert, E. (1996). Thermal Conductivity of a Thermosetting Advanced Composite During its Cure , Journal of Thermophysics and Heat Transfer, 10(3): 467-474 .