Periodic heat conduction in a solid homogeneous finite cylinder |
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| Authors: | GE Cossali |
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| Affiliation: | 1. College of Information Science and Engineering, Huaqiao University, Xiamen City 361021, China;2. Interface Analysis Centre, University of Bristol, Tyndall Avenue, Bristol BS2 1TL, UK;3. Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK;1. Université de Lyon, France;2. Bâtiment Sadi Carnot, 9 rue de la physique, INSA de Lyon, 69621 Villeurbanne Cedex, France;3. Bâtiment B. Pascal, 7 Avenue Jean Capelle 69621 Villeurbanne cedex, France;4. INSA de Lyon, Lyon F-69621, France;5. Bâtiment Copernic, 5 bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France;1. Innovative Sensor Technology IST AG, Stegruetistrasse 14, 9642 Ebnat-Kappel, Switzerland;2. Laboratory for Gas Sensors, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Koehler-Allee 102, 79110 Freiburg, Germany;3. Fraunhofer Institute for Physical Measurement Techniques IPM, Heidenhofstrasse 8, 79110 Freiburg, Germany |
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| Abstract: | Analytic solution of the steady periodic, non-necessarily harmonic, heat conduction in a homogeneous cylinder of finite length and radius is given in term of Fourier transform of the fluctuating temperature field. The solutions are found for quite general boundary conditions (first, second and third kind on each surface) with the sole restriction of uniformity on the lateral surface and radial symmetry on the bases. The thermal quadrupole formalism is used to obtain a compact form of the solution that can be, with some exception, straightforwardly extended to multi-slab composite cylinders. The limiting cases of infinite thickness and infinite radius are also considered and solved. |
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