A hyperbolic microscopic model and its numerical scheme for thermal analysis in an N-carrier system |
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| Authors: | Weizhong Dai |
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| Affiliation: | 1. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran;2. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran;3. Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran 19839, Iran;1. Department of Mathematics, Princeton University, Princeton, NJ 08544, USA;2. Mathematisches Institut, Friedrich-Schiller Universität Jena, Ernst-Abbé Platz 2, 07743 Jena, Germany;3. Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany;1. School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, PR China;2. Department of Mechanical Engineering, University of Minnesota-Twin Cities, 111 Church St. SE, Minneapolis, MN 55455, United States;1. Department of Computer Science, Loughborough University, LE11 3TU, Loughborough, UK;2. Department of Computer Science, University of Central Florida, Orlando, FL, USA;3. IT University of Copenhagen, Copenhagen, Denmark |
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| Abstract: | We extend the concept of the well-known hyperbolic two-step model for micro heat transfer to the case of energy exchanges in a generalized N-carrier system. The model satisfies an energy estimate and hence is well-posed. Based on this result, a finite difference scheme is developed for solving the hyperbolic microscopic model. The scheme is shown to satisfy a discrete analogue of the energy estimate, implying that it is unconditionally stable. Finally, the scheme is tested by an example. The difference between the hyperbolic model and the corresponding parabolic model for a multi-carrier system is also compared. |
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