A hybrid Green’s function method for the hyperbolic heat conduction problems |
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Authors: | Tzer-Ming Chen |
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Affiliation: | 1. Department of Computer Science, Federal University of Juiz de Fora, 36036-330 Juiz de Fora, MG, Brazil;2. Department of Civil Engineering, COPPE/Federal University of Rio de Janeiro, 21945-970 Rio de Janeiro, RJ, Brazil;3. School of Engineering and Design, Brunel University, UB8 3PH Uxbridge, London, UK;4. Postgraduate Program in Computational Modeling, Federal University of Juiz de Fora, 36036-900 Juiz de Fora, MG, Brazil;1. College of Engineering and Science, Louisiana Tech University, Ruston, LA 71272, USA;2. Department of Mathematics, Southeast University, Nanjing, PR China;1. Department of Mechanical Engineering, University of Canterbury, Christchurch, NZ, New Zealand;2. Institute for Thermo-Fluid Dynamics, Hamburg University of Technology, Hamburg-Harburg, DE, Germany |
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Abstract: | The present study is devoted to propose a hybrid Green’s function method to investigate the hyperbolic heat conduction problems. The difficulty of the numerical solutions of hyperbolic heat conduction problems is the numerical oscillation in the vicinity of sharp discontinuities. In the present study, we have developed a hybrid method combined the Laplace transform, Green’s function and ε-algorithm acceleration method for solving time dependent hyperbolic heat conduction equation. From one- to three-dimensional problems, six different examples have been analyzed by the present method. It is found from these examples that the present method is in agreement with the Tsai-tse Kao’s solutions Tsai-tse Kao, Non-Fourier heat conduction in thin surface layers, J. Heat Transfer 99 (1977) 343–345] and does not exhibit numerical oscillations at the wave front. The propagation of the two- and three-dimensional thermal wave becomes so complicated because it occur jump discontinuities, reflections and interactions in these numerical results of the problem and it is difficult to find the analytical solutions or the result of other study to compare with the solutions of the present method. |
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