An improved model for predicting thermal contact resistance at multi-layered rock interface

Abstract

This study proposes a general imperfect thermal contact model to predict the thermal contact resistance at the interface among multi-layered composite structures. Based on the Green-Lindsay (GL) thermoelastic theory, semi-analytical solutions of temperature increment and displacement of multi-layered composite structures are obtained by using the Laplace transform method, upon which the effects of thermal resistance coefficient, partition coefficient, thermal conductivity ratio and heat capacity ratio on the responses are studied. The results show that the generalized imperfect thermal contact model can realistically describe the imperfect thermal contact problem. Accordingly, it may degenerate into other thermal contact models by adjusting the thermal resistance coefficient and partition coefficient.

Keywords

multi-layered structures / general thermal contact model / thermal contact resistance / GL thermoelastic theory / Laplace transform

References

[1] Man Y, Yang H-X, Diao N-R, et al. . A new model and analytical solutions for borehole and pile ground heat exchangers [J]. International Journal of Heat and Mass Transfer. 2010, 53(13–14): 2593-2601

[2] Akilu S, Padmanabhan E, Sun Z. A review of transport mechanisms and models for unconventional tight shale gas reservoir systems [J]. International Journal of Heat and Mass Transfer. 2021, 175: 121125

[3] Khan S A, Hayat T, Alsaedi A. Simultaneous features of soret and dufour in entropy optimized flow of Reiner-rivlin fluid considering thermal radiation [J]. International Communications in Heat and Mass Transfer. 2022, 137: 106297

[4] Turkyilmazoglu M. MHD fluid flow and heat transfer due to a shrinking rotating disk [J]. Computers & Fluids. 2014, 90: 51-56

[5] Zanganeh M, Yeganeh-Bakhtiary A, Abd Wahab A K. Lagrangian coupling two-phase flow model to simulate current-induced scour beneath marine pipelines [J]. Applied Ocean Research. 2012, 38: 64-73

[6] Zhang Z, Han T, Zhang H-G, et al. . Heat transfer model of miniature heat pipe embedded in marine cabinet [J]. Journal of Coastal Research. 2019, 97(sp1): 103

[7] Park D S, Shin M B, Seo Y K. Heat-transfer characteristics of subsea pipelines embedded in multilayered soils [J]. SPE Journal. 2020, 25(3): 1128-1139

[8] Biot M A. Thermoelasticity and irreversible thermodynamics [J]. Journal of Applied Physics. 1956, 27(3): 240-253

[9] Lord H, Shulman Y. A generalized dynamical theory of thermoelasticity [J]. Journal of the Mechanics and Physics of Solids. 1967, 15: 299-309

[10] Alagappan P, Rajagopal K R, Srinivasa A R. Wave propagation due to impact through layered polymer composites [J]. Composite Structures. 2014, 115: 1-11

[11] Green A E, Lindsay K A. Thermoelasticity [J]. Journal of Elasticity. 1972, 2(1): 1-7

[12] Green A E, Naghdi P M. Thermoelasticity without energy dissipation [J]. Journal of Elasticity. 1993, 31(3): 189-208

[13] Yu Y J, Xue Z-N, Li C-L, et al. . Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity [J]. Composite Structures. 2016, 146: 108-113

[14] Xue Z-N, Yu Y-J, Tian X-G. Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating [J]. Waves in Random and Complex Media. 2017, 27(3): 440-457

[15] Xue Z-N, Cao G-Q, Liu J-L. Size-dependent thermoelasticity of a finite bi-layered nanoscale plate based on nonlocal dual-phase-lag heat conduction and Eringen’s nonlocal elasticity [J]. Applied Mathematics and Mechanics. 2021, 42(1): 1-16

[16] Bachher M, Sarkar N, Lahiri A. Fractional order thermoelastic interactions in an infinite porous material due to distributed time-dependent heat sources [J]. Meccanica. 2015, 50(8): 2167-2178

[17] Sherief H, Abd El-Latief A M. Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity [J]. International Journal of Mechanical Sciences. 2013, 74: 185-189

[18] Sherief H H, Abd El-Latief A M. A one-dimensional fractional order thermoelastic problem for a spherical cavity [J]. Mathematics and Mechanics of Solids. 2015, 20(5): 512-521

[19] YOUSSEF H M, EL-BARY A A. Thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity [J]. Mathematical Problems in Engineering, 2006(1): 087940. DOI: https://doi.org/10.1155/mpe/2006/87940.

[20] Hosseini-Tehrani P, Eslami M R, Shojaeefard M H. Generalized thermoelastic analysis of layer interface excited by pulsed laser heating [J]. Engineering Analysis with Boundary Elements. 2003, 27(9): 863-869

[21] Yu J-G, Wu B, He C-F. Guided thermoelastic wave propagation in layered plates without energy dissipation [J]. Acta Mechanica Solida Sinica. 2011, 24(2): 135-143

[22] El-Bary A A, Youssef H M. Thermal shock problem for one dimensional generalized thermoelastic layered composite material [J]. Mathematical and Computational Applications. 2006, 11(2): 103-110

[23] Amiri Delouei A, Kayhani M H, Norouzi M. Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates [J]. International Journal of Heat and Mass Transfer. 2012, 55(15): 4427-4436 16

[24] Akbarzadeh A H, Chen Z T. Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2013, 227(4): 744-759

[25] Abd El-Latief A M, Khader S E. Fractional model of thermoelasticity for a half-space overlaid by a thick layer [J]. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift Für Angewandte Mathematik und Mechanik. 2015, 95(5): 511-518

[26] Liu C-Q, Yu W, Chen C, et al. . Remarkably reduced thermal contact resistance of graphene/olefin block copolymer/paraffin form stable phase change thermal interface material [J]. International Journal of Heat and Mass Transfer. 2020, 163: 120393

[27] Yovanovich M M. Four decades of research on thermal contact, gap, and joint resistance in microelectronics [J]. IEEE Transactions on Components and Packaging Technologies. 2005, 28(2): 182-206

[28] Tavman I H. Effective thermal conductivity of granular porous materials [J]. International Communications in Heat and Mass Transfer. 1996, 23(2): 169-176

[29] Weidenfeld G, Weiss Y, Kalman H. A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression [J]. Granular Matter. 2004, 6(2): 121-129

[30] Jackson R L, Bhavnani S H, Ferguson T P. A multiscale model of thermal contact resistance between rough surfaces [J]. Journal of Heat Transfer. 2008, 130(8): 1

[31] Roshankhah S, Santamarina J C. Engineered granular materials for heat conduction and load transfer in energy geotechnology [J]. Géotechnique Letters. 2014, 4(2): 145-150

[32] Gori F, Marino C, Pietrafesa M. Experimental measurements and theoretical predictions of the thermal conductivity of two phases glass beads [J]. International Communications in Heat and Mass Transfer. 2001, 28(8): 1091-1102

[33] Wallen B M, Smits K, Sakaki T, et al. . Thermal conductivity of binary sand mixtures evaluated through full water content range [J]. Soil Science Society of America Journal. 2016, 80: 592-603

[34] BALASUBRAMANIAN G, PURI I K. Heat conduction across a solid-solid interface: Understanding nanoscale interfacial effects on thermal resistance [J]. 2011, 99(1): 013116. DOI: https://doi.org/10.1063/1.3607477.

[35] Tio K K, Kok Chuan T. Thermal resistance of two solids in contact through a cylindrical joint [J]. International Journal of Heat and Mass Transfer. 1998, 41(13): 2013-2024

[36] Kek-Kiong T, Sadhal S S. Thermal constriction resistance: Effects of boundary conditions and contact geometries [J]. International Journal of Heat and Mass Transfer. 1992, 35(6): 1533-1544

[37] Xue Z-N, Yu Y-J, Tian X-G. Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions [J]. International Journal of Mechanical Sciences. 2015, 99: 179-186

[38] Xue Z-N, Yu Y-J, Li C-L, et al. . Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions [J]. Journal of Thermal Stresses. 2016, 39(9): 1017-1034

[39] Li W-G, Li D-J, Zhang C-Z, et al. . Modelling the effect of temperature and damage on the fracture strength of ultra-high temperature ceramics [J]. International Journal of Fracture. 2012, 176(2): 181-188

[40] Li W-G, Wang R-Z, Li D-Y, et al. . Effect of the cooling medium temperature on the thermal shock resistance of ceramic materials [J]. Materials Letters. 2015, 138: 216-218

[41] Lor W B, Chu H S. Effect of interface thermal resistance on heat transfer in a composite medium using the thermal wave model [J]. International Journal of Heat and Mass Transfer. 2000, 43(5): 653-663

[42] Xue Z-N, Yu Y-J, Tian X-G. Transient responses of multi-layered structures with interfacial conditions in the generalized thermoelastic diffusion theory [J]. International Journal of Mechanical Sciences. 2017, 131: 63-74

[43] Wen M-J, Wang K-H, Wu W-B, et al. . Dynamic response of bilayered saturated porous media based on fractional thermoelastic theory [J]. Journal of Zhejiang University: Science A. 2021, 22(12): 992-1004

[44] Wen M-J, Tian Y, Wu W-B, et al. . Influence of thermal contact resistance on dynamic response of bilayered saturated porous strata [J]. Journal of Central South University. 2022, 29(6): 1823-1839

[45] Carr E J, March N G. Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions [J]. Applied Mathematics and Computation. 2018, 333: 286-303

[46] Crump K S. Numerical inversion of Laplace transforms using a Fourier series approximation [J]. Journal of the ACM. 1976, 23(1): 89-96

RIGHTS & PERMISSIONS

Central South University