SYMMETRY AND ASYMMETRY MODEL FOR THERMAL CONDUCTIVITY IN POROUS MEDIA
Abstract
This paper focuses on determining thermal conductivity in porous media using symmetry and asymmetry models. Since porous media are not uniform and homogeneous in most of the cases, anisotropy must be taken into account, what derives in the application of an asymmetry model as thermal gradients are not equal in all directions. The paper demonstrates that, under certain conditions, isotropic conditions, therefore, symmetry model can be applied to non-homogeneous or uniform porous media. The paper also proves that as external power and temperature increases the symmetry model is no longer valid, being necessary to apply the asymmetry model that takes into account convection effects. The comparison between symmetry and asymmetry model results allows determining the influence of convective cells. The proposed algorithms can be used to calculate thermal conductivity at any conditions, say external power or operational temperature. Thermal conductivity at the starting up point can be determined using symmetry model, using the asymmetry model for higher temperatures. The modeling has been validated comparing experimental data and estimated values, within a very good accuracy, higher than 99% in all cases.
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A. Alrtimia, M. Rouainiaa & S. Haighb (2016) Thermal conductivity of a sandy soil
Applied Thermal Engineering, Volume 106
Blackwell D.D., Steele J.L. (1989) Thermal Conductivity of Sedimentary Rocks: Measurement and Significance. In: Naeser N.D., McCulloh T.H. (eds) Thermal History of Sedimentary Basins. Springer, New York, NY.
P. Ocłoń, M. Bittelli, P. Cisek, E. Kroener, M.Pilarczyk, D. Taler, R.V. Rao, A. Vallati (2016) The performance analysis of a new thermal backfill material for underground power cable system. Applied Thermal Engineering, 108, pp. 233-250
P. Ocłoń, P. Cisek, D. Taler, M. Pilarczyk, T.Szwarc (2015) Optimizing of the underground power cable bedding using momentum-type particle swarm optimization method Energy, 92, pp. 230-239
P. Ocłoń, P. Cisek, M. Pilarczyk, D. Taler (2015) Numerical simulation of heat dissipation processes in underground power cable system situated in thermal backfill and buried in a multilayered soil Energy Conversion and Management, 95, pp. 352-370.
P. Ocłoń, D. Taler, P. Cisek, M. Pilarczyk (2015) Fem Based Thermal Analysis of Underground Power Cables Located in Backfills Made of Different Materials Strength of Materials, 47 (5), pp. 770- 780
P. Cisek, P. Ocłoń, M. Pilarczyk (2014) Thermal analysis of operating conditions for The 400 kV underground power cable transmission line as a power plant delivery system. Rynek Energii; 114:70–7 [in polish]
E. Kroener, A. Vallati, M. Bittelli (2014) Numerical simulation of coupled heat, liquid water and water vapor in soils for heat dissipation of underground electrical power cables. App Therm Eng; 70:510–23 (2014)
Banks D. (2008) An introduction to thermogeology: ground source heating and cooling. Oxford: Blackwell Publishing Ltd.
British Standards Institution (1990) Methods of test for soils for civil engineering purposes. London: BSI.
Mitchell, J K, Kao (1978) Measurement of Soil Thermal Resistivity. Journal of Geotechnical and Geoenvironmental Engineering Volume: 104. Publisher: American Society of Civil Engineers
Nan Zhang & Zhaoyu Wang (2017) Review of soil thermal conductivity and predictive models International Journal of Thermal Sciences
CH Liu, D Zhou, H Wu (2012) Measurement and prediction of temperature effects of thermal conductivity of soils. Chinese Journal of Geotechnical Engineering
Dong, Y., McCartney, J.S. & Lu, N. (2015) Geotechnical and Geological Engineering. Springer. 33: 207. https://doi.org/10.1007/s10706-015-9843-2
W. Woodside and J. H. Messmer (1961) Thermal Conductivity of Porous Media. I. Unconsolidated Sands. Journal of Applied Physics 32, 1688; https://doi.org/10.1063/1.1728419
Jianting Zhu (2019) A cell model of effective thermal conductivity for saturated porous media. International Journal of Heat and Mass Transfer. Volume 138, p.1054-1060
H. T. Aichlmayr, F. A. Kulacki (2006) The Effective Thermal Conductivity of Saturated Porous Media. Advances in Heat Transfer Volume 39, p. 377-460
Yuqing Shen, Peng Xua, , Binqi Rao, Boming Yu (2020) A generalized thermal conductivity model for unsaturated porous media with fractal geometry. International Journal of Heat and Mass Transfer. Volume 152. 119540
M. Ghalambaz, A. Behseresht, J. Behseresht, A. Chamkha (2015) Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media. Advanced Powder Technology.Volume 26, Issue 1, p.224-235
B. Usowicz, J. Lipiec, J. B. Usowicz (2008) Thermal conductivity in relation to porosity and hardness of terrestrial porous media. Planetary and Space ScienceVolume 56, Issues 3–4, p.438-447
Hangming Shen, Qian Ye, Guoxiang Meng (2017) Anisotropic fractal model for the effective thermal conductivity of random metal fiber porous media with high porosity. Volume 381. Issue 37, p.3193-3196
Tongjun Miao, Sujun Cheng, Aimin Chen, Boming Yu (2016) Analysis of axial thermal conductivity of dual-porosity fractal porous media with random fractures. International Journal of Heat and Mass Transfer. Volume 102, p.884-890
Arash Behrang, Saeed Taheri, Apostolos Kantzas (2016) A hybrid approach on predicting the effective thermal conductivity of porous and nanoporous media. International Journal of Heat and Mass Transfer. Volume 98, p.52-59
H. Davarzani, M. Marcoux, M. Quintard (2011) Effect of solid thermal conductivity and particle–particle contact on effective thermodiffusion coefficient in porous media. International Journal of Thermal Sciences. Volume 50, Issue 12, p. 2328-2339
Milad Tajik Jamal-Abad, Seyfollah Saedodin, Mohammad Aminy (2018) Variable conductivity in forced convection for a tube filled with porous media: A perturbation solution. Ain Shams Engineering Journal. Volume 9, Issue 4, p.689-696
Saied Afshari, Seyed Hossein Hejazi, Apostolos Kantzas (2019) Pore-level modeling of effective longitudinal thermal dispersion in non-isothermal flows through granular porous media. Chemical Engineering Science. Volume 199, p. 451-462
Fuguo Tong, Lanru Jing, Robert W. Zimmerman (2009) An effective thermal conductivity model of geological porous media for coupled thermo-hydro-mechanical systems with multiphase flow. International Journal of Rock Mechanics and Mining Sciences. Volume 46, Issue 8, December 2009, p.1358-1369
T. H. Bauer (1993) A general analytical approach toward the thermal conductivity of porous media. International Journal of Heat and Mass Transfer. Volume 36, Issue 17, p. 4181-4191
Jianlong Kou, Fengmin Wu, Hangjun Lu, Yousheng Xu, Fuquan Song (2009) The effective thermal conductivity of porous media based on statistical self-similarity. Physics Letters A. Volume 374, Issue 1, p-62-65
Kristian B. Kiradjiev, Svenn Anton Halvorsen, Robert A. Van Gorder, Sam D. Howison (2019) Maxwell-type models for the effective thermal conductivity of a porous material with radiative transfer in the voids. International Journal of Thermal Sciences. Volume 14, Article 106009
Mazhar Hussain, Wen-Quan Tao (2020) Thermal conductivity of composite building materials: A pore scale modeling approach. International Journal of Heat and Mass Transfer. Volume 14, Article 118691
Jean Côté, Jean-Marie Konrad (2009) Assessment of structure effects on the thermal conductivity of two-phase porous geomaterials. International Journal of Heat and Mass Transfer. Volume 52, Issues 3–4, p.796-804
A. Mirabolghasemi, A. H. Akbarzadeh, D. Rodrigue, D. Therriault (2019) Thermal conductivity of architected cellular metamaterials. Acta Materialia.Volume 174, p. 61-80
S. Jayachandran, K. S. Reddy (2019) Estimation of effective thermal conductivity of packed beds incorporating effects of primary and secondary parameters. Thermal Science and Engineering Progress. Volume 11, p. 392-408
Juan Pablo M. Florez, Marcia B.H. Mantelli, Gustavo G.V. Nuernberg (2013) Effective thermal conductivity of sintered porous media: Model and experimental validation. International Journal of Heat and Mass Transfer. Volume 66, p.868-878
H. J. Xu (2020) Thermal transport in microchannels partially filled with micro-porous media involving flow inertia, flow/thermal slips, thermal non-equilibrium and thermal asymmetry. International Communications in Heat and Mass Transfer. Volume 110, Article 104404
Yunus A. Çengel and Afshin J. Ghajar (2015). Heat and Mass Transfer Fundamentals & Applications. Mc Graw Hill, 5th edition
Serth R.W. (2007) Process heat transfer: principles and applications. Academic Press. 1st edition
Guruprasad Alva, Yaxue Lin, Guiyin Fang (2018) An overview of thermal energy storage systems. Energy. Volume 144, p. 341-378
Mina Rouhani, Wendell Huttema, Majid Bahrami (2018) Effective thermal conductivity of packed bed adsorbers: Part 1 – Experimental study. International Journal of Heat and Mass Transfer. Volume 123, p. 1204-1211
A. D. Duchkov, L. S. Sokolova, D. E. Ayunov, P. A. Yan (2016) Thermal conductivity of the Bazhenovo Formation rocks in the Salym area (West Siberian Plate). Russian Geology and Geophysics. Volume 57, Issue 7, p. 1078-1089
E. Popov, A. Trofimov, A. Goncharov, S. Abaimov, I. Sevostianov (2018) Technique of rock thermal conductivity evaluation on core cuttings and non-consolidated rocks. International Journal of Rock Mechanics and Mining Sciences. Volume 108, p. 15-22
D. Barry-Macaulay, A. Bouazza, R. M. Singh, B. Wang, P. G. Ranjith (2013) Thermal conductivity of soils and rocks from the Melbourne (Australia) region. Engineering Geology. Volume 164, p. 131-138
F. Chen, A. Giraud, D. Grgic, K. Kalo (2017) A composite sphere assemblage model for porous oolitic rocks: Application to thermal conductivity. Journal of Rock Mechanics and Geotechnical Engineering. Volume 9, Issue 1, p. 54-61
Mohsen Hajihassani, Aminaton Marto, Nima Khezri, Roohollah Kalatehjari (2015) Indirect measure of thermal conductivity of rocks through adaptive neuro-fuzzy inference system and multivariate regression analysis. Measurement. Volume 67, p. 71-77
M. G. Alishaev, I. M. Abdulagatov, Z. Z. Abdulagatova (2012) Effective thermal conductivity of fluid-saturated rocks: Experiment and modeling. Engineering Geology. Volumes 135–136, p. 24-39
Sven Fuchs, Felina Schütz, Hans-Jürgen Förster, Andrea Förster (2013) Evaluation of common mixing models for calculating bulk thermal conductivity of sedimentary rocks: Correction charts and new conversion equations. Geothermics. Volume 47, p. 40-52
C. Gruescu, A. Giraud, F. Homand, D. Kondo, D. P. Do (2007) Effective thermal conductivity of partially saturated porous rocks. International Journal of Solids and Structures. Volume 44, Issues 3–4, p. 811-833
Ming Luo, James R. Wood, Lawrence M. Cathles (1994) Prediction of thermal conductivity in reservoir rocks using fabric theory. Journal of Applied Geophysics. Volume 32, Issue 4, p. 321-334
Stuart Kenneth Haigh (2012) Thermal conductivity of sands. University of Cambridge. Research Gate
Hu Wen, Jun-hui Lu, Yang Xiao, Jun Deng (2015) Temperature dependence of thermal conductivity, diffusion and specific heat capacity for coal and rocks from coalfield. Thermochimica Acta. Volume 619, p. 41-47
Jishi Geng, Qiang Sun, Yuchun Zhang, Liwen Cao, Yuliang Zhang (2018) Temperature dependence of the thermal diffusivity of sandstone. Journal of Petroleum Science and Engineering. Volume 164, p. 110-116
Hans-Dieter Vosteen, Rüdiger Schellschmidt (2003) Influence of temperature on thermal conductivity, thermal capacity and thermal diffusivity for different types of rock. Physics and Chemistry of the Earth, Parts A/B/C. Volume 28, Issues 9–11, p. 499-509
Weiqiang Zhang, Qiang Sun, Shuqing Hao, Jishi Geng, Chao Lv (2016) Experimental study on the variation of physical and mechanical properties of rock after high temperature treatment. Applied Thermal Engineering. Volume 98, p. 1297-1304
Anne M. Hofmeister (2007) Pressure dependence of thermal transport properties. The National Academy of Sciences (USA)
Jesse D. Merriman, Alan G. Whittington, and Anne M. Hofmeister (2017) Re-evaluating Thermal Conductivity from the Top Down: Thermal Transport Properties of Crustal Rocks as a Function of Temperature, Mineralogy and Texture. Proceedings of the 42nd Workshop on Geothermal Reservoir Engineering. Stanford University, Stanford, California, February 13-15, SGP-TR-212
H.S.Carslaw and J.C.Jaeger (1959) Conduction of Heat in Solids. Clarendon Press, 2nd edition. Oxford
Donald A. Nield and Adrian Bejan (2006) Duke Convection in Porous Media Third Edition. Durham, North Carolina, USA. Springer Science USA.Library of Congress Control Number:2005932308 .13 digit ISBN: 978-0387-29096-6
Handbook of POROUS MEDIA Second Edition Edited by Kambiz Vafai. International Standard Book Number-13: 978-1-4398-8557-4 (eBook – PDF). Scholarly articles for Handbook of POROUS MEDIA Second Edition Edited by Kambiz Vafai. 2005.
http://materias.fi.uba.ar/6731/Tablas/Tabla6.pdf
J.M.Molina, R.Prieto,J.Narciso, E.Louis (2009) The effect of porosity on the thermal conductivity of Al–12 wt.% Si/SiC composites. Scripta Materialia, Elsevier
Jean Côté, Jean-Marie Konrad (2005)A generalized thermal conductivity model for soils and construction materials. Canadian Geotechnical Journal
Karol Pietrak, Tomasz S. Wisniewski (2015) A review of models for elective thermal conductivity of composite materials, journal of Power Technologies 95 (1) 14–24
B Usowicz, J Lipiec, JB Usowicz (2008) Thermal conductivity in relation to porosity and hardness of terrestrial porous media.Planetary and Space Science, Elsevier
Yongjin Feng, Boming Yu, Mingqing Zou and Duanming Zhang (2004) A generalized model for the effective thermal conductivity of porous media based on self-similarity. J. Phys. D. Journal of Physics D: Applied Physics 37 3030–3040
William Woodside (1959) Calculation of the thermal conductivity of porous media Canadian Journal of Physics, 37(7): 798-808
Shan Xiong Chen (2008) Thermal conductivity of sands. Springer
DOI: https://doi.org/10.37591/joge.v7i2.3846
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