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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 34, 1998 - Issue 2
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Original Articles

FINITE-DIFFERENCE SOLUTION OF HYPERBOLIC HEAT CONDUCTION WITH TEMPERATURE-DEPENDENT PROPERTIES

B. Pulvirenti Dipartimento di lngegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Viale Risorgimento 2. 1-40136, Bologna, Italy
,
A. Barletta Dipartimento di lngegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Viale Risorgimento 2. 1-40136, Bologna, Italy
&
E. Zanchini Dipartimento di lngegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Viale Risorgimento 2. 1-40136, Bologna, Italy
Pages 169-183 | Received 19 Nov 1997, Accepted 17 Mar 1998, Published online: 15 Mar 2007

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Masoud Molaei Najafabadi, Ardalan Shafiei Ghazani & Hassan Basirat Tabrizi. (2013) Numerical Simulation of Non-Fourier Temperature Behavior of Functionally Graded Materials in a Slab with Surface Radiation. Numerical Heat Transfer, Part A: Applications 63:3, pages 226-243.
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J. Li, P. Cheng, G. P. Peterson & J. Z. Xu. (2005) RAPID TRANSIENT HEAT CONDUCTION IN MULTILAYER MATERIALS WITH PULSED HEATING BOUNDARY. Numerical Heat Transfer, Part A: Applications 47:7, pages 633-652.
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Nima Noormohammadi & Nazanin Pirhaji Khouzani. (2023) A New Formulation of the Scaled Boundary Finite Element Method for Heterogeneous Media: Application to Heat Transfer Problems. Acta Mechanica Solida Sinica.
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Hamdy M. Youssef & Eman A. N. Al-Lehaibi. (2023) General generalized thermoelasticity theory (GGTT). Journal of Thermal Analysis and Calorimetry 148:13, pages 5917-5926.
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Xiang Li, Haolong Chen, Zhanli Liu, Ziming Yan & Zhuo Zhuang. (2022) Identifying Varying Thermal Diffusivity of Inhomogeneous Materials Based on a Hybrid Physics-Informed Neural Network. International Journal of Applied Mechanics 14:07.
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Whye-Teong Ang. (2021) A boundary element and radial basis function method for the Cattaneo–Vernotte equation in anisotropic media with spatially varying and temperature dependent properties. Partial Differential Equations in Applied Mathematics 4, pages 100138.
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M. Baghban & M. B. Ayani. (2018) Heat-Flux Estimation in a Nonlinear Heat Conduction Problem with a Dual-Phase-Lag Model. Journal of Thermophysics and Heat Transfer 32:1, pages 196-204.
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Wael Mahmoud, Moustafa S. Abou-Dina, Amr R. El Dhaba, Ahmed F. Ghaleb & Enaam K. Rawy. 2018. Generalized Models and Non-classical Approaches in Complex Materials 1. Generalized Models and Non-classical Approaches in Complex Materials 1 505 516 .
Peng Li, Jun Liu, Gao Lin, Pengchong Zhang & Guotao Yang. (2017) A NURBS-based scaled boundary finite element method for the analysis of heat conduction problems with heat fluxes and temperatures on side-faces. International Journal of Heat and Mass Transfer 113, pages 764-779.
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Shan Lu, Jun Liu, Gao Lin & Pengchong Zhang. (2017) Modified scaled boundary finite element analysis of 3D steady-state heat conduction in anisotropic layered media. International Journal of Heat and Mass Transfer 108, pages 2462-2471.
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Mojtaba Baghban & Mohammad Bagher Ayani. (2016) Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy. Journal of the Brazilian Society of Mechanical Sciences and Engineering 39:5, pages 1479-1489.
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Mohammad Hossein Bazyar & Abbas Talebi. (2015) Scaled boundary finite-element method for solving non-homogeneous anisotropic heat conduction problems. Applied Mathematical Modelling 39:23-24, pages 7583-7599.
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Hai-Dong WangHai-Dong Wang. 2014. Theoretical and Experimental Studies on Non-Fourier Heat Conduction Based on Thermomass Theory. Theoretical and Experimental Studies on Non-Fourier Heat Conduction Based on Thermomass Theory 1 20 .
B. L. Wang & J. E. Li. (2013) Thermal shock resistance of solids associated with hyperbolic heat conduction theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469:2153, pages 20120754.
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Bao-Lin Wang. (2013) Transient thermal cracking associated with non-classical heat conduction in cylindrical coordinate system. Acta Mechanica Sinica 29:2, pages 211-218.
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D.M. Chang & B.L. Wang. (2012) Transient thermal fracture and crack growth behavior in brittle media based on non-Fourier heat conduction. Engineering Fracture Mechanics 94, pages 29-36.
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B.L. Wang & J.C. Han. (2012) A crack in a finite medium under transient non-Fourier heat conduction. International Journal of Heat and Mass Transfer 55:17-18, pages 4631-4637.
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B.L. Wang & J.C. Han. (2012) Non-Fourier heat conduction in layered composite materials with an interface crack. International Journal of Engineering Science 55, pages 66-75.
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B.L. Wang, J.C. Han & Y.G. Sun. (2012) A finite element/finite difference scheme for the non-classical heat conduction and associated thermal stresses. Finite Elements in Analysis and Design 50, pages 201-206.
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BaoLin Wang & JieCai Han. (2012) Fracture mechanics associated with non-classical heat conduction in thermoelastic media. Science China Physics, Mechanics and Astronomy 55:3, pages 493-504.
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Bao-Lin Wang & Jie-Cai Han. (2010) A finite element method for non-Fourier heat conduction in strong thermal shock environments. Frontiers of Materials Science in China 4:3, pages 226-233.
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Andrea Pietro Reverberi, Patrizia Bagnerini, Luigi Maga & Agostino Giacinto Bruzzone. (2008) On the non-linear Maxwell–Cattaneo equation with non-constant diffusivity: Shock and discontinuity waves. International Journal of Heat and Mass Transfer 51:21-22, pages 5327-5332.
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Shengjun Su & Weizhong Dai. (2006) Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source. International Journal of Heat and Mass Transfer 49:17-18, pages 2793-2801.
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Kuo-Chi Liu. (2006) Numerical simulation for non-linear thermal wave. Applied Mathematics and Computation 175:2, pages 1385-1399.
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S. Su, W. Dai, P.M. Jordan & R.E. Mickens. (2005) Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation. International Journal of Heat and Mass Transfer 48:11, pages 2233-2241.
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R.J Goldstein, E.R.G Eckert, W.E Ibele, S.V Patankar, T.W Simon, T.H Kuehn, P.J Strykowski, K.K Tamma, A Bar-Cohen, J.V.R Heberlein, J.H Davidson, J Bischof, F.A Kulacki, U Kortshagen & S Garrick. (2001) Heat transfer: a review of 1998 literature. International Journal of Heat and Mass Transfer 44:2, pages 253-366.
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S. Kiwan, M. Al-Nimr & M. Al-Sharo'a. (2000) Trial solution methods to solve the hyperbolic heat conduction equation. International Communications in Heat and Mass Transfer 27:6, pages 865-876.
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