Abstract
An experimental setup for 3ω method with a constant current source and two differential amplifiers was built to measure the thermal conductivity and the volumetric heat capacity of single polyacrylonitrile (PAN)-based carbon fiber. In complement to a well-known analytical thermal model, a numerical one was developed that can check the validity of the analytical one and can also take into account the effect of convective heat loss on the measurements. A detailed sensitivity analysis of the unknown parameters was presented that would finally help in the better design of the setup for 3ω method. The tests were performed under vacuum and atmospheric pressure for chromel wire as a reference sample and under vacuum for two types of PAN-based carbon fiber. Detailed measurements were performed displaying the influence of convective loss and the thermal contact resistance between fiber and copper electrodes on the estimation of thermal properties of carbon fiber.
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References
Sweeting RD, Liu XL. Measurement of thermal conductivity for fibre-reinforced composites. Compos Part A Appl Sci Manuf. 2004;35:933–8.
Selvakumar M, Ramkumar T, Chandrasekar P. Thermal characterization of titanium–titanium boride composites. J Therm Anal Calorim. 2019;136:419–24. https://doi.org/10.1007/s10973-019-08014-0.
Manocha LM, Warrier A, Manocha S, Sathiyamoorthy D, Banerjee S. Thermophysical properties of densified pitch based carbon/carbon materials-I. Bidirectional composites. Carbon. 2006;44:488–95.
Siddiqui MOR, Sun D. Development of experimental setup for measuring the thermal conductivity of textiles. Cloth Text Res J. 2018;36:215–30.
Gallego NC, Edie DD, Ntasin LN, Ervin VJ. Modeling the thermal conductivity of carbon fibers. Carbon. 2000;38:1003–10.
Craddock JD, Burgess JJ, Edrington SE, Weisenberger MC. Method for direct measurement of on-axis carbon fiber thermal diffusivity using the laser flash technique. J Therm Sci Eng Appl. 2016;9:014502. https://doi.org/10.1115/1.4034853.
Yamane T, Katayama SI, Todoki M, Hatta I. Thermal diffusivity measurement of single fibers by an ac calorimetric method. J Appl Phys. 1996;80:4358–65.
Wang JL, Gu M, Zhang X, Song Y. Thermal conductivity measurement of an individual fibre using a T type probe method. J Phys D Appl Phys. 2009;42:105502. https://doi.org/10.1088/0022-3727/42/10/105502
Pradere C, Batsale JC, Goyhénèche JM, Pailler R, Dilhaire S. Thermal properties of carbon fibers at very high temperature. Carbon. 2009;47:737–43.
Liu J, Qu W, Xie Y, Zhu B, Wang T, Bai X, et al. Thermal conductivity and annealing effect on structure of lignin-based microscale carbon fibers. Carbon. 2017;121:35–47. https://doi.org/10.1016/j.carbon.2017.05.066.
Lu L, Yi W, Zhang DL. 3 ω method for specific heat and thermal conductivity measurements. Rev Sci Instrum. 2001;72:2996–3003.
Tian T, Cole KD. Anisotropic thermal conductivity measurement of carbon-fiber/epoxy composite materials. Int J Heat Mass Transf. 2012;55:6530–7. https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.059.
Boussatour G, Cresson PY, Genestie B, Joly N, Brun JF, Lasri T. Measurement of the thermal conductivity of flexible biosourced polymers using the 3-omega method. Polym Test. 2018;70:503–10. https://doi.org/10.1016/j.polymertesting.2018.07.026.
Schiffres SN, Malen JA. Improved 3-omega measurement of thermal conductivity in liquid, gases, and powders using a metal-coated optical fiber. Rev Sci Instrum. 2011;82:064903. https://doi.org/10.1063/1.3593372.
Gauthier S, Giani A, Combette P. Gas thermal conductivity measurement using the three-omega method. Sens Actuators A Phys. 2013;195:50–5. https://doi.org/10.1016/j.sna.2012.12.032.
Zhao L, Luo Y, Huang X, Zhou X, Hebibul R, Ding J, et al. A novel microsensor for measuring thermal conductivity of fluid based on three omega method. Rev Sci Instrum. 2019;90:015002. https://doi.org/10.1063/1.5053835.
Wang ZL, Tang DW, Zhang WG. Simultaneous measurements of the thermal conductivity, thermal capacity and thermal diffusivity of an individual carbon fibre. J Phys D Appl Phys. 2007;40:4686–90.
Pradère C, Goyhénèche JM, Batsale JC, Dilhaire S, Pailler R. Thermal diffusivity measurements on a single fiber with microscale diameter at very high temperature. Int J Therm Sci. 2006;45:443–51.
Xing C, Jensen C, Munro T, White B, Ban H, Chirtoc M. Accurate thermal property measurement of fine fibers by the 3-omega technique. Appl Therm Eng. 2014;73:315–22.
Hou J, Wang X, Vellelacheruvu P, Guo J, Liu C, Cheng HM. Thermal characterization of single-wall carbon nanotube bundles using the self-heating 3ω technique. J Appl Phys. 2006;100:124314. https://doi.org/10.1063/1.2402973.
Kaviany M. Principles of heat transfer. New York: Wiley; 2002.
Boetcher SKS. Natural convection transfer from horizontal cylinders. In: Natural convection from circular cylinders. SpringerBriefs in applied sciences and technology. Cham: Springer. https://doi.org/10.1007/978-3-319-08132-8.
Ediss GA. Effect of vacuum pressure on the thermal loading of the ALMA cryostat. Natl Radio Astron Obs. 2006;554:1–3.
Chapelle E, Garnier B, Bourouga B. Interfacial thermal resistance measurement between metallic wire and polymer in polymer matrix composites. Int J Therm Sci. 2009;48:2221–7. https://doi.org/10.1016/j.ijthermalsci.2009.05.001.
Milošević ND, Raynaud M, Maglić KD. Estimation of thermal contact resistance between the materials of double-layer sample using the laser flash method. Inverse Probl Eng. 2002;10:85–103.
Sundqvist B. Thermal diffusivity and thermal conductivity of Chromel, Alumel, and Constantan in the range 100–450 K. J Appl Phys. 1992;72:539–45.
Omega Engineering. Physical Properties of Thermoelement Materials. https://www.omega.com/techref/pdf/z016.pdf. Accessed 1 Jan 2019.
Data sheet Torayca T300B. http://www.toraycfa.com/pdfs/T300DataSheet.pdf. Accessed 1 Jan 2019.
Data sheet Torayca T800H. https://www.toraycma.com/file_viewer.php?id=4463. Accessed 1 Jan 2019.
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The authors would like to thanks J. Aubril for the discussions and quality of his technical realizations.
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Mishra, K., Garnier, B., Le Corre, S. et al. Accurate measurement of the longitudinal thermal conductivity and volumetric heat capacity of single carbon fibers with the 3ω method. J Therm Anal Calorim 139, 1037–1047 (2020). https://doi.org/10.1007/s10973-019-08568-z
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DOI: https://doi.org/10.1007/s10973-019-08568-z