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A truly meshless method formulation for analysis of non-Fourier heat conduction in solids | ||
| Journal of Computational & Applied Research in Mechanical Engineering (JCARME) | ||
| مقاله 8، دوره 6، شماره 1 - شماره پیاپی 11، اسفند 2016، صفحه 75-89 اصل مقاله (1.12 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22061/jcarme.2016.522 | ||
| نویسنده | ||
| Isa Ahmadi* | ||
| Advanced Materials and Computational Mechanics Lab., Department of Mechanical Engineering, University of Zanjan, P.O.Box: 45371-38791, Zanjan, Iran | ||
| تاریخ دریافت: 19 مهر 1394، تاریخ بازنگری: 04 فروردین 1395، تاریخ پذیرش: 15 فروردین 1395 | ||
| چکیده | ||
| The non-Fourier effect in heat conduction is important in strong thermal environments and thermal shock problems. Generally, commercial FE codes are not available for analysis of non-Fourier heat conduction. In this study, a meshless formulation is presented for the analysis of the non-Fourier heat conduction in the materials. The formulation is based on the symmetric local weak form of the second-order non-Fourier heat conduction equation in terms of the temperature. Using the local weak form of heat transfer equations in the sub-domains, the governing equation of the non-Fourier heat conduction is discretized in the space domain to the second order ordinary differential equations for the time. The discretized equations are integrated into the time domain with an appropriate finite difference method. The fictitious numerical oscillations are completely suppressed from the front of temperature waves in the presented method. An analytical series solution is developed for the non-Fourier heat transfer in one-dimensional heat transfer for special boundary conditions and the accuracy of presented numerical meshless method is validated by comparison of the results of the numerical meshless solution and the series solution. The numerical results are presented for non-Fourier heat conduction for various Vernotte numbers and boundary conditions and the results are compared with the results of the classical Fourier heat conduction. | ||
| کلیدواژه‌ها | ||
| Meshless method؛ Non-Fourier heat conduction؛ Temperature waves؛ Heat propagation؛ Analytical solution | ||
| مراجع | ||
|
[1] V. Peshkov, “Second sound in helium II”, J. Phys. USSR, Vol. 8, No.1, pp. 381-388, (1944).
[2] C. C. Ackerman, and R. A. Guyer, “Temperature pulse in dielectric solids”, Ann. Phys., Vol. 50, No. 1, pp. 128-185, (1968).
[3] K. Mitra, S. Kumar, A. Vedaraz, and M. K. Moallemi, “Experimental evidence of hyperbolic heat conduction in processed meat”, ASME J. Heat Transfer, Vol. 117, No. 3, pp. 568-573,(1995).
[4] Y. S. Xu and Z. Y. Guo, “Heat wave phenomena in IC chips”, Int J Heat Mass Transfer, Vol. 38, No. 15, pp. 2919-2922, (1995).
[5] C. Cattaneo, “Sur une forme de l’equation de la chaleur eliminant le paradoxe d’ine propagation instantanee”, C. R. Acad. Sci., Vol. 247, pp. 431-433, (1958).
[6] P. Vernotte, “Les paradoxes de la theorie continue de l’equation de la chaleur”, C. R. Acad. Sci., Vol. 46, No. 22, pp. 3154-3155, (1958).
[7] J. C. Maxwell, “On the dynamical theory of gases”, Philos. Trans. Royal Soc. London, Vol. 157, No. 1, pp. 49-88, (1867).
[8] M. N. Ozisik, D. Y. Tzou, “On the wave theory in heat conduction”, ASME J. Heat Transfer, Vol. 116, No. 3, pp. 526-535, (1994).
[9] W. Kaminski, “Hyperbolic heat conduction equation for materials with a nonhomogenous inner structure”, ASME J. Heat Transfer, Vol. 112, No. 3, pp. 555-560, (1990).
[10] H. Herving, and K. Beckert, “Experimental evidence about the controversy concerning Fourier and non-Fourier heat conduction in materials with a nonhomogeneous inner structure”, Heat and mass Transfer, Vol. 36, No. 5, pp. 387-392, (2000).
[11] W. Roetzel, N. Putra and S. K. Das, “Experiment and analysis of non-fourier conduction in materials with non-homogeneous inner structure”, Int. J. therm. Sci., Vol. 42, No. 3, pp. 541-552, (2003).
[12] E. Ruckenstein, and C. A. Petty, “On the aging of supported metal catalyst due to hot spots”, Chemical Engineering Science, Vol. 27, No. 5, pp. 937-946, (1972).
[13] R. Ocone, and G. Astarita, “Continuous and discontinuous models for transport phenomena in polymers”, AIChE Journal, Vol. 33, No. 3, pp. 423-435, (1987).
[14] A. M. Mullis, “Rapid solidification in the framework of hyperbolic conduction model”, Int. J. Heat Mass Transfer, Vol. 40, No. 17, pp. 4085-4097, (1997).
[15] V. Taitel, “On the parabolic, hyperbolic and discrete formulation of the heat conduction equation”, Int. J. Heat Mass Transfer, Vol. 15, No. 2, pp. 369-371, (1972).
[16] K. J. Baumeister, and T. D. Hamill, “Hyperbolic Heat-Conduction Equation—A Solution for the Semi-Infinite Body Problem”, ASME J. Heat Transfer, Vol. 91, No. 4, pp. 543-548, (1969).
[17] M. N. Ozisik, and B. Vick, “Propagation and reflection of thermal waves in a finite medium”, Int. J. Heat Mass Transfer, Vol. 27, No. 10, pp. 1845-1854, (1984).
[18] D. Y. Tzou, “Thermal Resonance Under Frequency Excitations”, ASME J. Heat Transfer, Vol. 114, No. 2, pp. 310-316, (1992)
[19] D. Y. Tzou, “Damping and Resonance Characteristics of Thermal Waves”, ASME J. Appl. Mech., Vol. 59, No. 4, pp. 862-867, (1992).
[20] J. I. Frankel, B. Vick and M. N. Ozisik, “Flux formulation of hyperbolic heat conduction”, J. Appl. Phys., Vol. 58, No, 1, pp. 3340-3345, (1985).
[21] J. Gembarovic and V. Majernik “Non-Fourier propagation of heat pulse in finite medium”, Int. J. Heat Mass Transfer, Vol. 31, pp. 1073-1081, (1988).
[22] Tang, D.W. and Araki N., “Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance”, Int. J Heat Mass Transfer. Vol. 39, No. 8, pp. 1585-1590, (1996).
[23] D. W. Tang, and N. Araki, “Non-Fourier Heat Conduction Behavior in Finite Mediums under Pulse Surface Heating”, Materials Sci. and Eng., Vol. 292, No. 2, pp. 173-178, (2000).
[24] G. F. Carey, and M. Tsai, “Hyperbolic heat transfer with reflection”, Numerical Heat Transfer Part A, Vol. 5, No. 3, pp. 309-327, (1982).
[25] D. E. Glass, M. N. Ozisik, D. S. McRae, and B. Vick, “The numerical solution of hyperbolic heat conduction”, Numerical Heat Transfer, Vol. 8, No. 4, pp. 497-504, (1985).
[26] D. E. Glass, M. N. Ozisik, D. S. McRae, B. Vick, “On the numerical solution of hyperbolic heat conduction”, Numerical Heat Transfer, Vol.8, No. 4, pp. 497-504, (1985).
[27] D. E. Glass, and M. N. Ozisik, “Non-Fourier Effects on Transient Temperature Resulting from Periodic On-Off Heat Flux”, Int. J. Heat Mass. Transfer, Vol. 30, No. 8 , pp. 1623-1631, (1987).
[28] H. Q. Yang, “Characteristics-based, high-order accurate and nonoscillatory numerical method for hyperbolic heat conduction”, Numerical Heat Transfer, Part B: Fundamentals, Vol. 18, No. 2, pp. 221-241, (1990).
[29] B. Pulvirenti, A. Barletta, and E. Zanchini “Finite-Difference Solution of Hyperbolic Heat Conduction with Temperature-Dependent Properties”, Numerical Heat Transfer A, Vol. 34, No. 2 , pp. 169-183, (1998).
[30] A. Kar, C. L. Chan, and J. Mazumder, “Comparative studies on nonlinear hyperbolic and parabolic heat conduction for various boundary conditions: analytic and numerical solutions”, ASME J. Heat Transfer, Vol. 114, No. 1, pp. 14-20, (1992).
[31] S. H. Pulko, A. J. Wilkinson, and A. Saidane, “TLM representation of the hyperbolic heat conduction equations”, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 15, No. 3, pp. 303-315, (2002).
[32] A. L. Koay, S. H. Pulko, and A. J. Wilkinson, “Reverse time TLM modeling of thermal problems described by the hyperbolic heat conduction equation", Numerical Heat Transfer, Part B: Fundamentals, Vol. 44, No. 4, pp. 347-363, (2003).
[33] K. K. Tamma and S. B. Railkar, “Specially tailored transfinite element formulations for hyperbolic heat conduction involving non-Fourier effects", Numerical Heat Transfer, Part B, Vol. 15, No. 2, pp. 211-226, (1989).
[34] M. T. Manzari, “A mixed approach to finite element analysis of hyperbolic heat conduction problems”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 8, No. 1, pp. 83-96, (1998)
[35] X. Ai, and B. Q. Li, “Discontinuous Finite Element Method for Non-Fourier Heat Conduction Problems”, Heat Transfer, Vol. 1, No. 1, pp. 237-243,(2003).
[36] W. Wu, and X. Li, “Application of the time discontinuous Galerkin finite element method to heat wave simulation”, International Journal of Heat and Mass Transfer, Vol. 49, No. 9-10, pp. 1679-1684, (2006).
[37] B. L. Wang, and J. C. Han, “A finite element method for non-Fourier heat conduction in strong thermal shock environments”, Front. Mater. Sci. China, Vol. 4, No. 3, pp. 226-233, (2010).
[38] S. C. Mishra, T. B. Pavan Kumar, and B. Mondal, “Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem”, Numerical Heat Transfer A, Vol. 54, No. 8, pp. 798-818, (2008).
[39] V. Vishwakarma, A. K. Das, and P. K. Das, “Analysis of non-Fourier heat conduction using smoothed particle hydrodynamics”, Applied Thermal Engineering, Vol. 31, No. 14-15, pp. 2963-2970, (2011).
[40] J. Sladek, V. Sladek, C. L. Tan, and S. N. Atluri, “Analysis of transient heat conduction in 3D anisotropic functionally graded solids by the MLPG”, CMES, Vol. 32, No. 3, pp. 161-174, (2008).
[41] X. H. Wu, and W. Q. Tao, “Meshless method based on the local weak-forms for steady-state heat conduction problems”, International Journal of Heat and Mass Transfer, Vol. 51, No. 11-12, pp. 3103-3112, (2008).
[42] S. Soleimani, M. Jalaal, H. Bararnia, E. Ghasemi, D. D. Ganji, and F. Mohammadi, “Local RBF-DQ method for two-dimensional transient heat conduction problem”, International Communications in Heat and Mass Transfer, Vol. 37, No. 9, pp. 1411-1418, (2010).
[43] Isa Ahmadi, and M. M. Aghdam, “Heat Transfer in Composite Materials using a New Truly Local Meshless Method”, International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 21, No. 3, pp. 293-309, (2011).
[44] S.N. Atluri and S. Shen, “The Meshless Local Petrov–Galerkin (MLPG) Method” Tech Science Press, Los Angeles, CA, (2002)
[45] D. Y. Tzou, J. K. Chen, “Thermal lagging in random media”, Journal of Thermophysics and Heat Transfer, Vol. 12, No. 4, pp. 567-574, (1998).
[46] A. Moosaie, “Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions”, Int. Commun. Heat Mass Transfer, Vol. 35, No. 1, pp. 103-111, (2008). | ||
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