Numerical calculation of the effective thermal properties of a composite by finite elements
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Published:
Jul 1, 2017
Keywords:
thermal conductivity, thermal diffusivity, thermal properties, composite, simulation, finite elements.
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Abstract
The development of new methods for determining the thermal properties of composite materials is always in constant progress. This study proposes a one-dimensional method for the numerical calculation of effective thermal conductivity and diffusivity in heterogeneous solid materials (composite), between [10--20 °C], using the program Solidworks 2016, which is based on the method of Finite Element Calculation. First, the temperature distribution is obtained as a function of the coordinate and time; then, the theoretical model, the Parabolic Heat Diffusion Equation in one dimension, is adjusted to the data obtained in the simulation to obtain the solution. Initially, the temperature distribution in a homogeneous solid copper bar, known material, is modeled under a constant heat flux at $x = L$, yielding thermal conductivity and diffusivity values in accordance with those reported in the literature, with a relative error of 0.01% and 0.7% respectively. Then, the temperature distribution is modeled in a heterogeneous solid bar based on copper (65.7%)--lead (34.3%) and, under the same heat flow condition, the simulated values of temperature in function of the time with which the effective thermal conductivity and diffusivity of this compound are calculated. The obtained results show consistency and reliability because they are within the range established by previous studies.
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Scientific Paper
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References
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[19] L. Sassi, F. Mzali, A. Jemnia and S. B. Nasrallah, “Hot-Wire Method for Measuring Effective Thermal Conductivity of Porous Media”, Journal of Porous Media, vol. 8, pp. 97-113, 2005.
[20] G. Peña et al., “Conductividad térmica efectiva promedio de polvos de arcillas Utilizadas en la industria cerámica del área metropolitana de san José de Cúcuta”. Revista Colombiana de Física, vol. 40, pp. 278-280, 2008.
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[22] D. R. Shonnard, S. Whitaker, "The effective thermal conductivity for a pointcontact porous medium: an experimental study", Inl. J. Hear Mass Transfer, vol. 32, pp. 503-512, 1989.
[23] N. Shemeena, B. Rajesh, A. Kurian, S. D. George, "Thermal conductivity measurement of organic solvents incorporated with silver nanoparticle using photothermal techniques," International Conference on Materials Science and Technology, India 2012
[24] J. Bravo, R. Guinovart, G. López, R. Rodríguez, F. J. Sabina, "Acerca de la homogeneización y propiedades efectivas de la ecuación del calor", Revista Visión Electrónica, vol. 7, pp. 149-159, 2013.
[25] S. Nie, C. Basaran, “A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds”, International Journal of Solids and Structures, vol. 42, pp. 79-91, 2005.
[26] G. Peña, A. Calderón, R. A. Muñoz, A. Florido, O. Flores, C. Falcony, "Influencia del tamaño de grano en la conductividad térmica a altas temperaturas en polvos aislantes de MgO", Superficies y Vacío, vol. 14, pp. 44-48, 2002.
[27] W. Benenson, J.W. Harris, H. Stöcker, H. Lutz, "Handbook of physics", 1ra ed., vol. 2, Ed. Springer-Verlag, USA, 2002, pp. 788-795.
[28] R. P. A. Rocha, M. E. Cruz, “Computation of the effective conductivity of unidirectional fibrous composites with an interfacial thermal resistance. Numerical Heat Transfer, Part A: Applications”, International Journal of Computation and Methodology, vol. 39, pp. 179-203, 2001.
[29] G. López, J. Bravo, M. E. Cruz, R. Guinovart, R. Rodríguez, "Cotas variacionales para coeficientes efectivos en compuestos con contacto imperfecto", Revista Visión Electrónica, vol. 7, pp. 53-64, 2013.
[2] A. Bouguerra, “Measurement of termal conductivity, thermal diffusivity and heat capacity of highly porous building materials using transient plane source technique”, International Communications in Heat and Mass Transfer, vol. 28, pp. 1065-1078, 2001.
[3] J. K. Carson, S. J. Lovatt, D. J. Tanner and A. C. Cleland, “Thermal conductivity bounds for isotropic porous materials”. International Journal of Heat and Mass Transfer, vol. 48, pp. 2150-2158, 2005.
[4] J. Hone, M. Whitney, C. Piskoti, A. Zettl, “Thermophysical properties of masonry units Accurate characterization”, The American Physical Society, vol. 59, pp. 2514-2516, 1999.
[5] J. A. P. Lima, E. Marín, O. Correa, M. G. da Silva, S. L. Cardoso, C. Gatts, C. E. Rezende, H. Vargas, L. C. M. Miranda, “Measurement of the thermal properties of liquids using a thermal wave interferometer”, Meas. Sci. Technol, vol. 11, pp. 1522-1526, 2000.
[6] L. Lira, O. J. González, E. Méndez, “Medición de la Conductividad Térmica 2008,” Simposio de Metrología SM2008-S4C2, México 2008.
[7] L. Lira, S. García, E. Méndez, E. González, “Conductividad Térmica en materiales,” Simposio de Metrología SM2010-Car-29, México 2010.
[8] A. Corona, G. Martínez, “Conducción térmica en una varilla de cobre”, Lat. Am. J. Phys. Educ. vol. 5, pp. 820-823, 2011.
[9] J. A. Gutiérrez, A. D. González, “Determinación experimental de conductividad térmica de materiales”, Avances en Energías Renovables y Medio Ambiente, vol.16, pp. 0841-0848, 2012.
[10] M. E. González, A. Denis, A. Soba, “Modelización de la conductividad térmica del UO2 y (U,Gd)O2 bajo irradiación. Implementación en el código Dionisio”, ANALES AFA, vol. 25, pp. 211-213, 2014.
[11] A. R. Warrier, R. Jayakrishnan, T. T. John, C. S. Kartha, K. P. Vijayakumar, “Study on optical, electronic and thermal properties of ?-In2S3 thin films using photothermal beam deflection technique” J Mater Sci: Mater Electron, DOI 10.1007/s10854-015-4201-y, 2015.
[12] K. Martínez, E. Marín, C. Glorieux, A. Lara, A. Calderónn, G. Peña, R. Ivanov, “Thermal diffusivity measurements in solids by photothermal infrared radiometry: Influence of convectioneradiation heat losses”, International Journal of Thermal Sciences, vol. 98, pp. 202-207, 2015.
[13] L. Velasco, L. Goyos, R. Delgado, L. Freire, "Instalación para medición de conductividad térmica en composites basados en residuos de biomasa", Enfoque UTE, vol.7, pp.69-81, 2016.
[14] N. Cobîrzan, A. A. Balog, B. Belean, G. Borodi, D. Dadârlat, M. Streza, "Thermophysical properties of masonry units: Accurate characterization by means of photothermal techniques and relationship to porosity and mineral composition", Construction and Building Materials, vol. 105, pp. 297–306, 2016.
[15] J. A. Ibáñez, F. J. Abellán, R. P. Valerdi, J. A. García, "Conductividad térmica de una barra de cobre. Estudio experimental del transitorio", Lat. Am. J. Phys. Educ., vol. 2, pp. 259-267, 2008.
[16] S. E. Gustafsson, “Transient plane source techniques for thermal conductivity and thermal diffusivity measurements of solid materials”, Review of Scientific Instruments, vol. 62, pp.797-804, 1991.
[17] R. L. Hamilton, O.K. Crosser, “Thermal Conductivity of Theory of Heterogeneus Two-Componet System”, I ? EC FUNDAMENTALS, vol. 1, pp. 187-190, 1962.
[18] Maxwell, J.C., “A trasient on Electricity and Magnetism” 2da ed., vol. 1, Ed. Clarendon Press, U.K., 1881, p. 435.
[19] L. Sassi, F. Mzali, A. Jemnia and S. B. Nasrallah, “Hot-Wire Method for Measuring Effective Thermal Conductivity of Porous Media”, Journal of Porous Media, vol. 8, pp. 97-113, 2005.
[20] G. Peña et al., “Conductividad térmica efectiva promedio de polvos de arcillas Utilizadas en la industria cerámica del área metropolitana de san José de Cúcuta”. Revista Colombiana de Física, vol. 40, pp. 278-280, 2008.
[21] N. Wakao, K. Kato, "Effective thermal conductivity of packed beds", Journal of Chemical Engineering of Japan”, vol. 2, pp.24-33, 1969.
[22] D. R. Shonnard, S. Whitaker, "The effective thermal conductivity for a pointcontact porous medium: an experimental study", Inl. J. Hear Mass Transfer, vol. 32, pp. 503-512, 1989.
[23] N. Shemeena, B. Rajesh, A. Kurian, S. D. George, "Thermal conductivity measurement of organic solvents incorporated with silver nanoparticle using photothermal techniques," International Conference on Materials Science and Technology, India 2012
[24] J. Bravo, R. Guinovart, G. López, R. Rodríguez, F. J. Sabina, "Acerca de la homogeneización y propiedades efectivas de la ecuación del calor", Revista Visión Electrónica, vol. 7, pp. 149-159, 2013.
[25] S. Nie, C. Basaran, “A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds”, International Journal of Solids and Structures, vol. 42, pp. 79-91, 2005.
[26] G. Peña, A. Calderón, R. A. Muñoz, A. Florido, O. Flores, C. Falcony, "Influencia del tamaño de grano en la conductividad térmica a altas temperaturas en polvos aislantes de MgO", Superficies y Vacío, vol. 14, pp. 44-48, 2002.
[27] W. Benenson, J.W. Harris, H. Stöcker, H. Lutz, "Handbook of physics", 1ra ed., vol. 2, Ed. Springer-Verlag, USA, 2002, pp. 788-795.
[28] R. P. A. Rocha, M. E. Cruz, “Computation of the effective conductivity of unidirectional fibrous composites with an interfacial thermal resistance. Numerical Heat Transfer, Part A: Applications”, International Journal of Computation and Methodology, vol. 39, pp. 179-203, 2001.
[29] G. López, J. Bravo, M. E. Cruz, R. Guinovart, R. Rodríguez, "Cotas variacionales para coeficientes efectivos en compuestos con contacto imperfecto", Revista Visión Electrónica, vol. 7, pp. 53-64, 2013.